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Theorem bnj334 29054
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj334  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ch  /\ 
ph  /\  ps  /\  th ) )

Proof of Theorem bnj334
StepHypRef Expression
1 bnj290 29051 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ch  /\  th  /\  ps ) )
2 bnj257 29048 . 2  |-  ( (
ph  /\  ch  /\  th  /\  ps )  <->  ( ph  /\ 
ch  /\  ps  /\  th ) )
3 bnj312 29053 . 2  |-  ( (
ph  /\  ch  /\  ps  /\ 
th )  <->  ( ch  /\ 
ph  /\  ps  /\  th ) )
41, 2, 33bitri 262 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ch  /\ 
ph  /\  ps  /\  th ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ w-bnj17 29027
This theorem is referenced by:  bnj345  29055  bnj518  29234  bnj916  29281  bnj929  29284
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 29028
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