MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3an6 Structured version   Unicode version

Theorem 3an6 1264
Description: Analog of an4 798 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
3an6  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th )  /\  ( ta 
/\  et ) )  <-> 
( ( ph  /\  ch  /\  ta )  /\  ( ps  /\  th  /\  et ) ) )

Proof of Theorem 3an6
StepHypRef Expression
1 an6 1263 . 2  |-  ( ( ( ph  /\  ch  /\ 
ta )  /\  ( ps  /\  th  /\  et ) )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )  /\  ( ta  /\  et ) ) )
21bicomi 194 1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th )  /\  ( ta 
/\  et ) )  <-> 
( ( ph  /\  ch  /\  ta )  /\  ( ps  /\  th  /\  et ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    /\ w3a 936
This theorem is referenced by:  poxp  6458  cusgra3v  21473  wfrlem4  25541  axcontlem8  25910  cgr3tr4  25986  f13dfv  28081
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 178  df-an 361  df-3an 938
  Copyright terms: Public domain W3C validator