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Theorem imdistand 429
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 → ((𝜓𝜒) → (𝜓𝜃)))

Proof of Theorem imdistand
StepHypRef Expression
1 imdistand.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 imdistan 426 . 2 ((𝜓 → (𝜒𝜃)) ↔ ((𝜓𝜒) → (𝜓𝜃)))
31, 2sylib 131 1 (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  imdistanda  430  pm5.32d  431  fconstfvm  5407  lbzbi  8648
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