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Theorem imdistanri 559
Description: Distribution of implication with conjunction. (Contributed by NM, 8-Jan-2002.)
Hypothesis
Ref Expression
imdistanri.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
imdistanri ((𝜓𝜑) → (𝜒𝜑))

Proof of Theorem imdistanri
StepHypRef Expression
1 imdistanri.1 . . 3 (𝜑 → (𝜓𝜒))
21com12 32 . 2 (𝜓 → (𝜑𝜒))
32impac 542 1 ((𝜓𝜑) → (𝜒𝜑))
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 197  df-an 383
This theorem is referenced by:  tc2  8782  prmodvdslcmf  15958  monmat2matmon  20849  cnextcn  22091  umgredg  26255  crctcshwlkn0lem5  26942  tpr2rico  30298  bj-snsetex  33282  bj-restuni  33382  poimirlem26  33768  seqpo  33875  isdrngo2  34089  pm10.55  39094  2pm13.193VD  39661
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