ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ancomsd Unicode version

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  569  ralxfrd  4383  rexxfrd  4384  poirr2  4931  smoel  6197  genprndl  7341  genprndu  7342  addcanprlemu  7435  leltadd  8221  lemul12b  8631  lbzbi  9420  dvdssub2  11546
  Copyright terms: Public domain W3C validator