Iago realizes that real proof of Desdemona's supposed infidelity is not necessary because mere suspicion is enough to feed Othello's jealousy. In the case of Othello, Iago will use the handkerchief Othello gave Desdemona in order to convince Othello that Desdemona's been cheating. (Remember, when Desdemona dropped her handkerchief by accident, Emilia picked it up and gave it to Iago. Iago says he's going to drop it for Cassio to find.) Even though the handkerchief is a mere "trifle, light as air," once Othello sees it in another man's possession, he'll think he has solid proof that Desdemona is unfaithful. When Iago says the handkerchief will be "as proofs of holy writ" to Othello, he means that Othello will see the handkerchief as the gospel truth that Desdemona's a cheater.
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