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Theorem imdistanri 696
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 33 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
32impac 626 1  |-  ( ( ps  /\  ph )  ->  ( ch  /\  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 371
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 189  df-an 373
This theorem is referenced by:  tc2  8229  prmodvdslcmf  14998  prmordvdslcmfOLD  15012  monmat2matmon  19840  cnextcn  21074  usgrarnedg  25103  tpr2rico  28720  bj-snsetex  31519  poimirlem26  31924  seqpo  32034  isdrngo2  32155  pm10.55  36620  2pm13.193VD  37205  usgrrnedg  38957
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