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Theorem imdistand 421
Description: Distribution of implication with conjunction (deduction rule). (Contributed by NM, 27-Aug-2004.)
Hypothesis
Ref Expression
imdistand.1 (φ → (ψ → (χθ)))
Assertion
Ref Expression
imdistand (φ → ((ψ χ) → (ψ θ)))

Proof of Theorem imdistand
StepHypRef Expression
1 imdistand.1 . 2 (φ → (ψ → (χθ)))
2 imdistan 418 . 2 ((ψ → (χθ)) ↔ ((ψ χ) → (ψ θ)))
31, 2sylib 127 1 (φ → ((ψ χ) → (ψ θ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  imdistanda  422  pm5.32d  423  fconstfvm  5322  lbzbi  8327
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