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Theorem imdistand 566
 Description: Distribution of implication with conjunction (deduction form). (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 563 . 2 ((𝜓 → (𝜒𝜃)) ↔ ((𝜓𝜒) → (𝜓𝜃)))
31, 2sylib 210 1 (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 386 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 199  df-an 387 This theorem is referenced by:  imdistanda  567  a2and  876  predpo  5942  unblem1  8487  cfub  9393  lbzbi  12066  poimirlem32  33980  ispridl2  34374  ispridlc  34406  lnr2i  38524  rfovcnvf1od  39133
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