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Theorem imdistand 724
 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 721 . 2 ((𝜓 → (𝜒𝜃)) ↔ ((𝜓𝜒) → (𝜓𝜃)))
31, 2sylib 207 1 (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383 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 196  df-an 385 This theorem is referenced by:  imdistanda  725  a2and  849  predpo  5615  unblem1  8097  cfub  8954  lbzbi  11652  poimirlem32  32611  ispridl2  33007  ispridlc  33039  lnr2i  36705  rfovcnvf1od  37318
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