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Mirrors > Home > ILE Home > Th. List > pm2.43 | GIF version |
Description: Absorption of redundant antecedent. Also called the "Contraction" or "Hilbert" axiom. Theorem *2.43 of [WhiteheadRussell] p. 106. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 15-Aug-2004.) |
Ref | Expression |
---|---|
pm2.43 | ⊢ ((𝜑 → (𝜑 → 𝜓)) → (𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.27 40 | . 2 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓)) | |
2 | 1 | a2i 11 | 1 ⊢ ((𝜑 → (𝜑 → 𝜓)) → (𝜑 → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: pm5.4 248 ralm 3498 |
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