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Divide into possible cases and prove each separately.
If A → C and B → C, then (A ∨ B) → CQuran's source: Muhammad, others, or God. Only divine authorship fits.
(Muhammad ∨ Others ∨ God) ∧ ¬Muhammad ∧ ¬Others → GodThe Quran's source must be one of three: Case 1 (Muhammad himself): He was unlettered, had no access to Jewish/Christian scriptures, could not have known historical details confirmed only recently. Case 2 (Other humans): No evidence exists, the style is unique to the Quran, and contemporaries denied helping him. Case 3 (Allah): This alone explains all features—the knowledge, eloquence, and perfection. Only divine authorship remains.
This is proof by cases: we list all possible sources, show each non-divine case fails to explain the evidence, and conclude by elimination that divine authorship is the only viable explanation.
This proof demonstrates the logical foundations of Islamic beliefs through rigorous philosophical methodology.