ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3ancomb Unicode version

Theorem 3ancomb 904
Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3ancomb  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ch  /\ 
ps ) )

Proof of Theorem 3ancomb
StepHypRef Expression
1 3ancoma 903 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
2 3anrot 901 . 2  |-  ( ( ps  /\  ph  /\  ch )  <->  ( ph  /\  ch  /\  ps ) )
31, 2bitri 177 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ch  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 102    /\ w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  3simpb  913  addcanprg  6771  elioore  8881
  Copyright terms: Public domain W3C validator