ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp11 Unicode version

Theorem simp11 1012
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp11  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ph )

Proof of Theorem simp11
StepHypRef Expression
1 simp1 982 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ph )
213ad2ant1 1003 1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th  /\  ta )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 963
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  df-3an 965
This theorem is referenced by:  simpl11  1057  simpr11  1066  simp111  1111  simp211  1120  simp311  1129  frecsuclem  6353
  Copyright terms: Public domain W3C validator