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Theorem ancomsd 267
Description: Deduction commuting conjunction in antecedent. (Contributed by NM, 12-Dec-2004.)
Hypothesis
Ref Expression
ancomsd.1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
Assertion
Ref Expression
ancomsd  |-  ( ph  ->  ( ( ch  /\  ps )  ->  th )
)

Proof of Theorem ancomsd
StepHypRef Expression
1 ancom 264 . 2  |-  ( ( ch  /\  ps )  <->  ( ps  /\  ch )
)
2 ancomsd.1 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
31, 2syl5bi 151 1  |-  ( ph  ->  ( ( ch  /\  ps )  ->  th )
)
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:  sylan2d  292  mpand  425  anabsi6  554  ralxfrd  4353  rexxfrd  4354  poirr2  4901  smoel  6165  genprndl  7297  genprndu  7298  addcanprlemu  7391  leltadd  8177  lemul12b  8587  lbzbi  9376  dvdssub2  11462
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