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Check all possible cases exhaustively.
P(x) is true for every possible xAll other systems fail to fully guide humanity; only Islam succeeds.
∀S ∈ {alternative systems}: ¬Complete(S) → Islam is necessaryWe exhaustively examine every alternative: (1) Secularism—no answers to "why are we here?" or "what happens after death?" (2) Christianity—original Injil lost; Trinity contradicts pure monotheism. (3) Judaism—restricted to Bani Israel, not a universal message. (4) Buddhism—no clear theology of God, lacks comprehensive law. (5) Hinduism—polytheistic, caste system contradicts human equality. Only Islam provides: preserved scripture, pure monotheism, universal message, and comprehensive guidance.
This is proof by exhaustion: we systematically examine every major alternative worldview, demonstrate each fails to provide complete guidance, and conclude Islam is necessary as the only comprehensive system.
This proof demonstrates the logical foundations of Islamic beliefs through rigorous philosophical methodology.