Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj258 Unicode version

Theorem bnj258 28410
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj258  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps  /\  th )  /\  ch ) )

Proof of Theorem bnj258
StepHypRef Expression
1 bnj257 28409 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ps  /\  th  /\  ch ) )
2 df-bnj17 28389 . 2  |-  ( (
ph  /\  ps  /\  th  /\  ch )  <->  ( ( ph  /\  ps  /\  th )  /\  ch ) )
31, 2bitri 241 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps  /\  th )  /\  ch ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    /\ w3a 936    /\ w-bnj17 28388
This theorem is referenced by:  bnj707  28461  bnj1019  28488  bnj556  28609  bnj594  28621  bnj1018  28671  bnj1110  28689
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  df-bnj17 28389
  Copyright terms: Public domain W3C validator