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Theorem imdistand 571
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 568 . 2 ((𝜓 → (𝜒𝜃)) ↔ ((𝜓𝜒) → (𝜓𝜃)))
31, 2sylib 219 1 (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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 208  df-an 397
This theorem is referenced by:  imdistanda  572  a2and  839  predpo  6159  unblem1  8758  cfub  9659  lbzbi  12324  cusgredgex  32265  poimirlem32  34805  ispridl2  35197  ispridlc  35229  lnr2i  39594  rfovcnvf1od  40228
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