From the Decretal Letter of Innocent I, to Victricius, Bishop of Rouen, A.D. 404

Decree VI. Lest he who has married a second wife become a cleric; because it is written: "the husband of one wife" ... And lest it be judged by some that, if perhaps someone accepted a wife before baptism and, she departing from this world, married another, this has been dismissed in baptism, he errs enough from the rule; because in baptism sins are dismissed, not the number of wives accepted abolished ...

Thus an end was imposed upon the question in which Jerome fought sharply for the opposite opinion (cf. his Letter LXIX to Oceanus), who also asked: "How are all sins drowned in the washing, if one wife (who had been accepted before baptism) floats above?" You have from Innocent the answer to this question.

Decree XI. What is worthy and modest and honorable, the Church altogether ought to hold: that priests and Levites not have intercourse with their wives, because they are occupied with the needs of the daily ministry.

Cf. Canon II of the Council of Carthage, A.D. 390. The Pontiff speaks only of the use of a marriage contracted before. He proposes the law in a gentle mode, but it is sufficiently established that a union of this sort is dishonorable if a Priest or Levite uses a marriage previously entered. Therefore this is altogether illicit; and for that reason it is said that the Church ought to hold this. Cf. Canon IX of Siricius from his letter to the Africans above.

Decree XII. Those who have spiritually married Christ and have merited to be veiled by a priest, if afterwards they have either publicly married or have corrupted themselves secretly, are not to be admitted to doing penance unless the one to whom they had joined themselves has departed from this world. For if this reckoning is kept concerning all, that any woman who, while her husband is living, has married another, is held an adulteress, and the license of doing penance is not conceded to her unless one of them shall have died, how much more must that woman be held to this, who had before joined herself to an immortal spouse and afterwards migrated to human nuptials?

Cf. the decrees of Siricius from Letter 10, Canon XVI of the Council of Toledo, Canon XI of the Council of Valence, Canons VI, XVIII, LX of Basil above.

Here Innocent rather openly betrays his opinion that these nuptials are null. This is clearer from the comparison made with what the following canon establishes concerning a virgin who indeed proposed to preserve virginity, but did not receive the veil. Her, some penance being imposed, he permits to remain in marriage.

Decree XIII. But those who, not yet covered with the sacred veil, nevertheless had promised always to remain in the virginal purpose, although they have not been veiled, if perhaps they have married, penance must be done by them for some time, because their pledge was held by God. For if among men a contract of good faith is accustomed to be dissolved by no reason, how much more ought that promise which the virgin has covenanted with God not be dissolved without vengeance?

You have that a simple vow of chastity is an impediment making nuptials illicit.