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Prove "If not B then not A" instead of "If A then B".
(¬B → ¬A) ↔ (A → B)If false prophet, would seek worldly gains; he rejected all gains.
¬Prophet → Seeks wealth; ¬Seeks wealth → ProphetThe contrapositive: if he were not a true prophet, he would seek worldly benefit from his claims. But he rejected every offer: Quraysh's wealth offers, kingship proposals, compromise suggestions. He chose persecution, poverty, and hardship over comfort. He died with his armor pawned to a Jewish merchant. His actions are the exact opposite of what a false prophet would do.
This is proof by contrapositive: instead of proving "true prophet → rejects worldly gain" directly, we observe "rejected worldly gain → true prophet." The complete absence of self-interest confirms authenticity.
This proof demonstrates the logical foundations of Islamic beliefs through rigorous philosophical methodology.