How do you know that Proctor has admitted something about his affair with Abigail to his wife Elizabeth?
In Act one, Parris questioned Abigail’s character and the events at the Proctor home that led to her dismissal. The reverend suspected that the reason behind her dismissal was beyond the ordinary. In addition, it was claimed that Elizabeth rarely went to church after firing Abigail because she would not interact with “something soiled”.
Subsequent events and conversations between Elizabeth and John further suggest that Elizabeth was aware of John’s relationship with Abigail. There was tension between John and Elizabeth as evident in Act two of the story. Elizabeth seemed suspicious of John’s visit to Salem and his late arrival back home. It was clear that Elizabeth and John had discussed the affair because John warned Elizabeth and further added that he had ended the affair. He also claimed that Elizabeth had not forgotten or forgiven him for the affair. He also stated that it was a mistake on his part to confess, instead, he should have dismissed her suspicions when she first tried to find out the truth.
Proctor: No more! I should have roared you down when first you told me your suspicion. But I wilted, and, like a Christian, I confessed. Confessed! Some dream I had must have mistaken you for God that day. But you’re not, you’re not, and let you remember it! Let you look sometimes for the goodness in me, and judge me not.
We know this for a few reasons.
First of all, we see that there is a great deal of tension between the two Proctors as soon as we see them together in Act II. This implies that John has told Elizabeth about his affair.
But then the way we can really know it is because they pretty much talk about it as they are arguing. John says he doesn't want Elizabeth to suspect him and she tells him he shouldn't earn her suspicion if he doesn't want it. Then she asks him if he would "falter" if he were going to hurt anyone but Abby. So clearly she knows there is something between them.
He then goes on to say that he confessed to her -- he doesn't say what he confessed, but in the context it's pretty clear.
Elizabeth dismissed Abigail as their servant very abruptly, and no other family in the village will take her. The atmospher at the Proctor home is cold, and John and Elizabeth have a difficult time even carrying on a civil conversation. Elizabeth questions John each time he has gone into town because she's afraid he's going to see Abigail. When Elizabeth discovers that Abigail admitted to John the girls are lying, Elizabeth wants John to go into town to tell the court. She feels John is hesitating to do so because he still has feelings for Abigail.