Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj422 Unicode version

Theorem bnj422 29056
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj422  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ch  /\ 
th  /\  ph  /\  ps ) )

Proof of Theorem bnj422
StepHypRef Expression
1 bnj345 29055 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( th  /\  ph  /\  ps  /\  ch ) )
2 bnj345 29055 . 2  |-  ( ( th  /\  ph  /\  ps  /\  ch )  <->  ( ch  /\ 
th  /\  ph  /\  ps ) )
31, 2bitri 240 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ch  /\ 
th  /\  ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ w-bnj17 29027
This theorem is referenced by:  bnj432  29057  bnj535  29238  bnj558  29250
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  df-bnj17 29028
  Copyright terms: Public domain W3C validator