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Theorem imdistanri 571
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 554 1 ((𝜓𝜑) → (𝜒𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397
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 206  df-an 398
This theorem is referenced by:  tc2  9733  prmodvdslcmf  16976  monmat2matmon  22308  cnextcn  23553  umgredg  28378  crctcshwlkn0lem5  29048  tpr2rico  32830  bj-snsetex  35782  bj-restuni  35916  poimirlem26  36452  seqpo  36553  isdrngo2  36764  pm10.55  43061  2pm13.193VD  43597
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