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Theorem pm2.43 56
Description: Absorption of redundant antecedent. Also called the "Contraction" or "Hilbert" axiom. Theorem *2.43 of [WhiteheadRussell] p. 106. (Contributed by NM, 10-Jan-1993.) (Proof shortened by Mel L. O'Cat, 15-Aug-2004.)
Assertion
Ref Expression
pm2.43 ((𝜑 → (𝜑𝜓)) → (𝜑𝜓))

Proof of Theorem pm2.43
StepHypRef Expression
1 pm2.27 42 . 2 (𝜑 → ((𝜑𝜓) → 𝜓))
21a2i 14 1 ((𝜑 → (𝜑𝜓)) → (𝜑𝜓))
Colors of variables: wff setvar 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  377  ax13b  1966  ralbidar  38117  rexbidar  38118
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