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Theorem bnj432 28741
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj432  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ch  /\  th )  /\  ( ph  /\  ps )
) )

Proof of Theorem bnj432
StepHypRef Expression
1 bnj422 28740 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ch  /\ 
th  /\  ph  /\  ps ) )
2 bnj256 28731 . 2  |-  ( ( ch  /\  th  /\  ph 
/\  ps )  <->  ( ( ch  /\  th )  /\  ( ph  /\  ps )
) )
31, 2bitri 240 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ch  /\  th )  /\  ( ph  /\  ps )
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    /\ w-bnj17 28711
This theorem is referenced by:  bnj605  28939  bnj600  28951
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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