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Theorem bnj422 29079
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
bnj422  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ch  /\ 
th  /\  ph  /\  ps ) )

Proof of Theorem bnj422
StepHypRef Expression
1 bnj345 29078 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( th  /\  ph  /\  ps  /\  ch ) )
2 bnj345 29078 . 2  |-  ( ( th  /\  ph  /\  ps  /\  ch )  <->  ( ch  /\ 
th  /\  ph  /\  ps ) )
31, 2bitri 241 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ch  /\ 
th  /\  ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ w-bnj17 29050
This theorem is referenced by:  bnj432  29080  bnj535  29261  bnj558  29273
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
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