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Theorem anabsi7 548
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)
Hypothesis
Ref Expression
anabsi7.1  |-  ( ps 
->  ( ( ph  /\  ps )  ->  ch )
)
Assertion
Ref Expression
anabsi7  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem anabsi7
StepHypRef Expression
1 anabsi7.1 . . 3  |-  ( ps 
->  ( ( ph  /\  ps )  ->  ch )
)
21anabsi6 547 . 2  |-  ( ( ps  /\  ph )  ->  ch )
32ancoms 264 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  syl2an23an  1235  nelrdva  2822  elunii  3658  ordelord  4208  onsucuni2  4380  funfveu  5318  fvelrn  5430  phplem3g  6572  prdisj  7051  gcdmultiplez  11288  dvdssq  11298
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