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Theorem imdistanri 723
 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 649 1 ((𝜓𝜑) → (𝜒𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383 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 196  df-an 385 This theorem is referenced by:  tc2  8501  prmodvdslcmf  15589  monmat2matmon  20448  cnextcn  21681  umgredg  25812  usgrarnedg  25913  tpr2rico  29286  bj-snsetex  32144  bj-restuni  32231  poimirlem26  32605  seqpo  32713  isdrngo2  32927  pm10.55  37590  2pm13.193VD  38161  crctcsh1wlkn0lem5  41017
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