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Theorem bnj257 28732
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj257  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ps  /\  th  /\  ch ) )

Proof of Theorem bnj257
StepHypRef Expression
1 ancom 437 . . 3  |-  ( ( ch  /\  th )  <->  ( th  /\  ch )
)
21anbi2i 675 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  <->  ( ( ph  /\  ps )  /\  ( th  /\  ch )
) )
3 bnj256 28731 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )
) )
4 bnj256 28731 . 2  |-  ( (
ph  /\  ps  /\  th  /\  ch )  <->  ( ( ph  /\  ps )  /\  ( th  /\  ch )
) )
52, 3, 43bitr4i 268 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ps  /\  th  /\  ch ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    /\ w-bnj17 28711
This theorem is referenced by:  bnj258  28733  bnj334  28738  bnj543  28925  bnj929  28968
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 28712
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