Do not trust fiance so should I leave him?

Maybe a month or so after we were engaged my fiance lied to me about another woman. I saw that she would post things on his facebook and just got a weird feeling about her. Anyway I looked at his phone (yes I am aware it was wrong) and saw he had been messaging this woman. They seemed to be friendly but almost crossing that boundary. I asked him (after I already knew he was talking to her) if he talked to her. He lied and said no. I asked again are you sure and again got the same answer. So I left and came back and asked him to let me see his phone. He showed me and suddenly those messages to her were gone. He deleted them and I then told him I knew cause I looked. He claims nothing happened that they just had a few conversations of no importance. I don’t believe him and the trust is broken. At this point should I just leave him?