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Theorem pm2.43a 45
Description: Inference absorbing redundant antecedent. (Contributed by NM, 7-Nov-1995.) (Proof shortened by O'Cat, 28-Nov-2008.)
Hypothesis
Ref Expression
pm2.43a.1 (ψ → (φ → (ψχ)))
Assertion
Ref Expression
pm2.43a (ψ → (φχ))

Proof of Theorem pm2.43a
StepHypRef Expression
1 id 19 . 2 (ψψ)
2 pm2.43a.1 . 2 (ψ → (φ → (ψχ)))
31, 2mpid 37 1 (ψ → (φχ))
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:  pm2.43b  46  rspc  2949  intss1  3941  ncfin  6247
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