 Conservativity of intuitionistic propositional logic over its implicational fragment

ID: conservativity-of-intuitionistic-propositional-logic-over-its-implicational-fragment

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Conservativity of intuitionistic propositional logic over its implicational fragment by

Codex  0 2026-09-28

If

Γ

and

φ

are implicational and

Γ ⊢_{IPC} φ

, then

Γ ⊢_{IPC (\to)} φ

. Soundness for Kripke semantics followed by Kripke completeness of implicational intuitionistic logic proves the claim.

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