Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj312 Structured version   Unicode version

Theorem bnj312 29076
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj312  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ps  /\ 
ph  /\  ch  /\  th ) )

Proof of Theorem bnj312
StepHypRef Expression
1 3ancoma 943 . . 3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ph  /\ 
ch ) )
21anbi1i 677 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th ) 
<->  ( ( ps  /\  ph 
/\  ch )  /\  th ) )
3 df-bnj17 29051 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps  /\  ch )  /\  th ) )
4 df-bnj17 29051 . 2  |-  ( ( ps  /\  ph  /\  ch  /\  th )  <->  ( ( ps  /\  ph  /\  ch )  /\  th ) )
52, 3, 43bitr4i 269 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ps  /\ 
ph  /\  ch  /\  th ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    /\ w3a 936    /\ w-bnj17 29050
This theorem is referenced by:  bnj334  29077  bnj563  29111  bnj953  29310
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 29051
  Copyright terms: Public domain W3C validator