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

Theorem imdistanri 689
Description: Distribution of implication with conjunction. (Contributed by NM, 8-Jan-2002.)
Hypothesis
Ref Expression
imdistanri.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
imdistanri  |-  ( ( ps  /\  ph )  ->  ( ch  /\  ph ) )

Proof of Theorem imdistanri
StepHypRef Expression
1 imdistanri.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21com12 29 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
32impac 619 1  |-  ( ( ps  /\  ph )  ->  ( ch  /\  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367
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 185  df-an 369
This theorem is referenced by:  tc2  8205  monmat2matmon  19617  cnextcn  20859  usgrarnedg  24801  tpr2rico  28347  bj-snsetex  31086  seqpo  31522  isdrngo2  31643  pm10.55  36122  2pm13.193VD  36734
  Copyright terms: Public domain W3C validator