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Theorem anabsi7 570
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 569 . 2  |-  ( ( ps  /\  ph )  ->  ch )
32ancoms 266 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:  syl2an23an  1277  nelrdva  2891  elunii  3741  ordelord  4303  onsucuni2  4479  funfveu  5434  fvelrn  5551  phplem3g  6750  prdisj  7312  gcdmultiplez  11720  dvdssq  11730
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