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Theorem imdistand 723
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 720 . 2 ((𝜓 → (𝜒𝜃)) ↔ ((𝜓𝜒) → (𝜓𝜃)))
31, 2sylib 206 1 (𝜑 → ((𝜓𝜒) → (𝜓𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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 195  df-an 384
This theorem is referenced by:  imdistanda  724  a2and  848  predpo  5601  unblem1  8074  cfub  8931  lbzbi  11608  poimirlem32  32407  ispridl2  32803  ispridlc  32835  lnr2i  36501  rfovcnvf1od  37114
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