If a woman says to a man, "You are my husband," and he says to her, "You are my wife," without intending a marriage contract, is this contract valid, and what is the reason for it not being considered a valid marriage formula?

We have not found any statements from scholars regarding the validity of a marriage contract through the man saying to the woman, "You are my wife," and her saying to him, "You are my husband." Moreover, among the most important conditions for marriage are the guardian and witnesses, both of which are absent here.