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Theorem imdistanri 722
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 648 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 195  df-an 384
This theorem is referenced by:  tc2  8475  prmodvdslcmf  15532  monmat2matmon  20387  cnextcn  21620  usgrarnedg  25676  tpr2rico  29089  bj-snsetex  31944  bj-restuni  32031  poimirlem26  32405  seqpo  32513  isdrngo2  32727  pm10.55  37390  2pm13.193VD  37961  umgredg  40370  crctcsh1wlkn0lem5  41016
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