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

Theorem bnj258 31583
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 31582 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ps  /\  th  /\  ch ) )
2 df-bnj17 31562 . 2  |-  ( (
ph  /\  ps  /\  th  /\  ch )  <->  ( ( ph  /\  ps  /\  th )  /\  ch ) )
31, 2bitri 249 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps  /\  th )  /\  ch ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369    /\ w3a 965    /\ w-bnj17 31561
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 967  df-bnj17 31562
This theorem is referenced by:  bnj707  31634  bnj1019  31660  bnj556  31780  bnj594  31792  bnj1018  31842  bnj1110  31860
  Copyright terms: Public domain W3C validator