MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3anrev Unicode version

Theorem 3anrev 945
Description: Reversal law for triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3anrev  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ch  /\  ps  /\ 
ph ) )

Proof of Theorem 3anrev
StepHypRef Expression
1 3ancoma 941 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
2 3anrot 939 . 2  |-  ( ( ch  /\  ps  /\  ph )  <->  ( ps  /\  ph 
/\  ch ) )
31, 2bitr4i 243 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ch  /\  ps  /\ 
ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ w3a 934
This theorem is referenced by:  3com13  1156  nnmcan  6648  odupos  14255  btwnswapid2  24713  colinbtwnle  24813  dualcat2  25887  frgra3v  28426  uunT11p2  28887  uunT12p5  28893  uun2221p2  28904  bnj345  29055  bnj1098  29131
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
  Copyright terms: Public domain W3C validator