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Theorem imdistanri 570
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 553 1 ((𝜓𝜑) → (𝜒𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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 397
This theorem is referenced by:  tc2  9739  prmodvdslcmf  16982  monmat2matmon  22333  cnextcn  23578  umgredg  28436  crctcshwlkn0lem5  29106  tpr2rico  32961  bj-snsetex  35930  bj-restuni  36064  poimirlem26  36600  seqpo  36701  isdrngo2  36912  pm10.55  43210  2pm13.193VD  43746
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