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Theorem bnj268 29135
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj268  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ch  /\  ps  /\  th ) )

Proof of Theorem bnj268
StepHypRef Expression
1 3ancomb 946 . . 3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ph  /\  ch  /\ 
ps ) )
21anbi1i 678 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th ) 
<->  ( ( ph  /\  ch  /\  ps )  /\  th ) )
3 df-bnj17 29113 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps  /\  ch )  /\  th ) )
4 df-bnj17 29113 . 2  |-  ( (
ph  /\  ch  /\  ps  /\ 
th )  <->  ( ( ph  /\  ch  /\  ps )  /\  th ) )
52, 3, 43bitr4i 270 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ch  /\  ps  /\  th ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360    /\ w3a 937    /\ w-bnj17 29112
This theorem is referenced by:  bnj543  29326  bnj929  29369  bnj1110  29413
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 179  df-an 362  df-3an 939  df-bnj17 29113
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