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Theorem imdistanri 572
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 555 1 ((𝜓𝜑) → (𝜒𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398
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 209  df-an 399
This theorem is referenced by:  tc2  9176  prmodvdslcmf  16375  monmat2matmon  21424  cnextcn  22667  umgredg  26915  crctcshwlkn0lem5  27584  tpr2rico  31148  bj-snsetex  34268  bj-restuni  34380  poimirlem26  34910  seqpo  35014  isdrngo2  35228  pm10.55  40691  2pm13.193VD  41227
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