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Theorem anabsan2 558
Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004.) (Revised by NM, 1-Jan-2013.)
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 539 . 2  |-  ( ( ps  /\  ( ph  /\ 
ps ) )  ->  ch )
32anabss7 557 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  anabss3  559  anandirs  567
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