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

Theorem ancomsd 266
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 263 . 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-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  sylan2d  289  mpand  421  anabsi6  548  ralxfrd  4312  rexxfrd  4313  poirr2  4857  smoel  6103  genprndl  7177  genprndu  7178  addcanprlemu  7271  leltadd  8022  lemul12b  8419  lbzbi  9200  dvdssub2  11281
  Copyright terms: Public domain W3C validator