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Prove base case, then assume n and show for n+1.
P(0) ∧ (P(k) → P(k+1)) → ∀n: P(n)All prophets brought consistent message, culminating in final revelation.
Base: Tawhid(P₁). Step: ∀n: Tawhid(Pₙ) → Tawhid(Pₙ₊₁). ∴ Tawhid(Muhammad)Base case: The earliest prophets (Adam, Noah) preached pure monotheism—worship Allah alone. Inductive step: Each subsequent prophet confirmed and built upon previous revelations: Abraham confirmed Noah, Moses confirmed Abraham, Jesus confirmed Moses. Pattern: Every prophet brought the same core message (tawhid) while adding relevant guidance for their time. Conclusion: Muhammad ﷺ follows this pattern, confirming all previous prophets while completing the message.
This is an inductive argument: we establish a base case (early prophets taught tawhid), show the pattern continues (each prophet confirms predecessors), and conclude the pattern extends to Muhammad ﷺ. The remarkable consistency across millennia and continents points to a single divine source.
This proof demonstrates the logical foundations of Islamic beliefs through rigorous philosophical methodology.