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Theorem anabsi7 581
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 580 . 2  |-  ( ( ps  /\  ph )  ->  ch )
32ancoms 268 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  syl2an23an  1299  nelrdva  2944  elunii  3812  ordelord  4378  onsucuni2  4560  funfveu  5524  fvelrn  5643  phplem3g  6850  prdisj  7482  gcdmultiplez  12005  dvdssq  12015
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