Because Elizabeth does not tell the truth about Proctor's affair with Abigail, her testimony proves that John is lying in court. Her testimony is unfair because Proctor is telling the truth, but the court does not believe him, and they test the truth of his words by bring his wife into the court and not allowing her any communication with him, she can't even look at him. Here is how it plays out.
In an effort to discredit Abigail Williams and shake the court's total belief in her credibility as the main witness in the witch trials, Proctor confesses to committing adultery with Abigail. He is trying to prove to the court that Abigail has a personal motive in condemning people as witches, particularly his wife, Elizabeth.
"Proctor says: She thinks to dance with me on my wife's grave! And well she might, for I though of her softly. God help me, I lusted and there is a promise in such sweat. But it is a whore's vengeance and you must see it." (Miller)
While John is giving this testimony, Elizabeth is in jail, they have not spoken since she was taken out of their home in chains and arrested. The court officials retrieve her so that she can corroborate his story, prove it is true by giving a second testimony with the same facts. She, however, by now, has softened to her husband, forgiven him for his sin against her and does not want to condemn him publicly for his adultery.
Elizabeth decides to lie to protect John's reputation and his good name. So when she is asked why she dismissed Abigail from her employment as a servant in their house, she does not tell the truth. Elizabeth is not allowed to look at or talk to her husband before or during her testimony, so she could not have known that he confessed willingly to the affair with Abigail. In an effort to keep their private lives private, Elizabeth skirts around the truth.
"Danforth: For what cause did you dismiss her?
"Elizabeth: Your honor I in that time I were sick. And my husband is a good and righteous man. I came to think he fancied her and so one night I lost my wits, I think and put her out on the highroad." (Miller)
"Danforth: To you own knowledge has John Proctor ever committed the crime of lechery?"
"Elizabeth: No sir." (Miller)