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Theorem bnj446 29019
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj446  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ps  /\  ch  /\  th )  /\  ph ) )

Proof of Theorem bnj446
StepHypRef Expression
1 bnj345 29016 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ph )  <->  ( ph  /\ 
ps  /\  ch  /\  th ) )
2 df-bnj17 28989 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ph )  <->  ( ( ps  /\  ch  /\  th )  /\  ph ) )
31, 2bitr3i 243 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ps  /\  ch  /\  th )  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    /\ w3a 936    /\ w-bnj17 28988
This theorem is referenced by:  bnj642  29054  bnj667  29058  bnj594  29221
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 28989
  Copyright terms: Public domain W3C validator