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

Theorem 3anrot 925
Description: Rotation law for triple conjunction. (Contributed by NM, 8-Apr-1994.)
Assertion
Ref Expression
3anrot  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ch  /\ 
ph ) )

Proof of Theorem 3anrot
StepHypRef Expression
1 ancom 262 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  <->  ( ( ps  /\  ch )  /\  ph ) )
2 3anass 924 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ( ps  /\  ch ) ) )
3 df-3an 922 . 2  |-  ( ( ps  /\  ch  /\  ph )  <->  ( ( ps 
/\  ch )  /\  ph ) )
41, 2, 33bitr4i 210 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ch  /\ 
ph ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103    /\ 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:  3ancomb  928  3anrev  930  3simpc  938  caovlem2d  5724  nnmcan  6158  modmulconst  10372
  Copyright terms: Public domain W3C validator