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Theorem imdistanri 573
 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 556 1 ((𝜓𝜑) → (𝜒𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399 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 210  df-an 400 This theorem is referenced by:  tc2  9217  prmodvdslcmf  16438  monmat2matmon  21524  cnextcn  22767  umgredg  27030  crctcshwlkn0lem5  27699  tpr2rico  31383  bj-snsetex  34680  bj-restuni  34792  poimirlem26  35363  seqpo  35465  isdrngo2  35676  pm10.55  41446  2pm13.193VD  41982
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