MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  imdistanri Structured version   Visualization version   GIF version

Theorem imdistanri 727
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 650 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 197  df-an 385
This theorem is referenced by:  tc2  8656  prmodvdslcmf  15798  monmat2matmon  20677  cnextcn  21918  umgredg  26078  crctcshwlkn0lem5  26762  tpr2rico  30086  bj-snsetex  33076  bj-restuni  33175  poimirlem26  33565  seqpo  33673  isdrngo2  33887  pm10.55  38885  2pm13.193VD  39453
  Copyright terms: Public domain W3C validator