ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp33 Unicode version

Theorem simp33 977
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
Assertion
Ref Expression
simp33  |-  ( (
ph  /\  ps  /\  ( ch  /\  th  /\  ta ) )  ->  ta )

Proof of Theorem simp33
StepHypRef Expression
1 simp3 941 . 2  |-  ( ( ch  /\  th  /\  ta )  ->  ta )
213ad2ant3 962 1  |-  ( (
ph  /\  ps  /\  ( ch  /\  th  /\  ta ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  simpl33  1022  simpr33  1031  simp133  1076  simp233  1085  simp333  1094
  Copyright terms: Public domain W3C validator