Objection 1. It would seem that irregularity is not contracted by marrying one who is not a virgin. For a man's own defect is a greater impediment to him than the defect of another. But if the man himself who marries is not a virgin he does not become irregular. Therefore much less does he if his wife is not a virgin.
Objection 2. Further, it may happen that a man marries a woman after corrupting her. Now, seemingly, such a man does not become irregular, since he has not divided his flesh among several, nor has his wife done so, and yet he marries a woman who is not a virgin. Therefore this kind of bigamy does not cause irregularity.
Objection 3. Further, no man can become irregular except voluntarily. But sometimes a man marries involuntarily one who is not a virgin, for instance when he thinks her a virgin and afterwards, by knowing her carnally, finds that she is not. Therefore this kind does not always cause irregularity.
Objection 4. Further, unlawful intercourse after marriage is more guilty than before marriage. Now if a wife, after the marriage has been consummated, has intercourse with another man, her husband does not become irregular, otherwise he would be punished for his wife's sin. Moreover, it might happen that, after knowing of this, he pays her the debt at her asking, before she is accused and convicted of adultery. Therefore it would seem that this kind of bigamy does not cause irregularity.
On the contrary, Gregory says (Regist. ii, ep. 37): "We command thee never to make unlawful ordinations, nor to admit to holy orders a bigamist, or one who has married a woman that is not a virgin, or one who is unlettered, or one who is deformed in his limbs, or bound to do penance or to perform some civil duty, or who is in any state of subjection."
I answer that, In the union of Christ with the Church unity is found on either side. Consequently whether we find division of the flesh on the part of the husband, or on the part of the wife, there is a defect of sacrament. There is, however, a difference, because on the part of the husband it is required that he should not have married another wife, but not that he should be a virgin, whereas on the part of the wife it is also required that she be a virgin. The reason assigned by those versed in the Decretals is because the bridegroom signifies the Church militant which is entrusted to the care of a bishop, and in which there are many corruptions, while the spouse signifies Christ Who was a virgin: wherefore virginity on the part of the spouse, but not on the part of the bridegroom, is required in order that a man be made a bishop. This reason, however, is expressly contrary to the words of the Apostle (Ephesians 5:25): "Husbands, love your wives, as Christ also loved the Church," which show that the bride signifies the Church, and the bridegroom Christ; and again he says (Ephesians 5:23): "Because the husband is the head of the wife, as Christ is the head of the Church." Wherefore others say that Christ is signified by the bridegroom, and that the bride signifies the Church triumphant in which there is no stain. Also that the synagogue was first united to Christ as a concubine; so that the sacrament loses nothing of its signification if the bridegroom previously had a concubine. But this is most absurd, since just as the faith of ancients and of moderns is one, so is the Church one. Wherefore those who served God at the time of the synagogue belonged to the unity of the Church in which we serve God. Moreover this is expressly contrary to Jeremiah 3:14, Ezekiel 16:8, Hosea 2:16, where the espousals of the synagogue are mentioned explicitly: so that she was not as a concubine but as a wife. Again, according to this, fornication would be the sacred sign [sacramentum] of that union, which is absurd. Wherefore heathendom, before being espoused to Christ in the faith of the Church, was corrupted by the devil through idolatry. Hence we must say otherwise that irregularity is caused by a defect in the sacrament itself. Now when corruption of the flesh occurs outside wedlock on account of a preceding marriage, it causes no defect in the sacrament on the part of the person corrupted, but it causes a defect in the other person, because the act of one who contracts marriage terminates not in himself, but in the other party, wherefore it takes its species from its term, which, moreover, in regard to that act, is the matter as it were of the sacrament. Consequently if a woman were able to receive orders, just as her husband becomes irregular through marrying one who is not a virgin, but not through his not being a virgin when he marries, so also would a woman become irregular if she were to marry a man who is not a virgin, but not if she were no longer a virgin when she married --unless she had been corrupted by reason of a previous marriage.
This suffices for the Reply to the First Objection.
Reply to Objection 2. In this case opinions differ. It is, however, more probable that he is not irregular, because he has not divided his flesh among several women.
Reply to Objection 3. Irregularity is not the infliction of a punishment, but the defect of a sacrament. Consequently it is not always necessary for bigamy to be voluntary in order to cause irregularity. Hence a man who marries a woman, thinking her to be a virgin, whereas she is not, becomes irregular by knowing her carnally.
Reply to Objection 4. If a woman commits fornication after being married, her husband does not become irregular on that account, unless he again knows her carnally after she has been corrupted by adultery, since otherwise the corruption of the wife nowise affects the marriage act of the husband. But though he be compelled by law to pay her the debt, or if he do so at her request, being compelled by his own conscience, even before she is convicted of adultery, he becomes irregular, albeit opinions differ on this point. However, what we have said is more probable, since here it is not a question of sin, but of signification only.
Source: Summa Theologica (New Advent)