What proof does he offer?
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Iago had his wife "borrow" the handkerchief from Desdemona. Iago is able to manipulate the handkerchief so that Othello comes to see it as a symbol of Desdemona herself, her devotion and finally her infidelity. The handkerchief is used as proof that she is cheating with Casio and making a cuckold out of Othello