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Theorem anabsan2 797
Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004.)
Hypothesis
Ref Expression
anabsan2.1  |-  ( (
ph  /\  ( ps  /\ 
ps ) )  ->  ch )
Assertion
Ref Expression
anabsan2  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem anabsan2
StepHypRef Expression
1 anabsan2.1 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ps ) )  ->  ch )
21an12s 778 . 2  |-  ( ( ps  /\  ( ph  /\ 
ps ) )  ->  ch )
32anabss7 796 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360
This theorem is referenced by:  anabss3  798  anandirs  806  lmodvsdi  15975  lmodvsdir  15976  lmodvsass  15977  lss0cl  16025  phlpropd  16888  mbfimasn  19528  metider  24291  2cshwmod  28279
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 179  df-an 362
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