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Divide into possible cases and prove each separately.
If A → C and B → C, then (A ∨ B) → CAmong all religions: corrupted, incomplete, or Islam. Only Islam remains pure.
(Corrupted_religions ∨ Incomplete_systems ∨ Islam) ∧ ¬Corrupted ∧ ¬Incomplete → IslamCase 1 (Previous revealed religions): Judaism—tribal, original Torah lost, not universally applicable. Christianity—original Injil lost, scriptures altered, contradictory doctrines (Trinity). Case 2 (Man-made systems): Secularism lacks spiritual guidance; philosophical systems contradict each other. Case 3 (Islam): Scripture perfectly preserved, message universal, doctrine consistent, guidance comprehensive. Only Islam survives examination.
This is proof by cases: we enumerate all possible sources of truth (previous religions, man-made systems, Islam), show each non-Islamic case fails on critical criteria, and conclude Islam is the true path by elimination.
This proof demonstrates the logical foundations of Islamic beliefs through rigorous philosophical methodology.