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Theorem bnj446 32867
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 32864 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ph )  <->  ( ph  /\ 
ps  /\  ch  /\  th ) )
2 df-bnj17 32837 . 2  |-  ( ( ps  /\  ch  /\  th 
/\  ph )  <->  ( ( ps  /\  ch  /\  th )  /\  ph ) )
31, 2bitr3i 251 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ps  /\  ch  /\  th )  /\  ph ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369    /\ w3a 973    /\ w-bnj17 32836
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-bnj17 32837
This theorem is referenced by:  bnj642  32902  bnj667  32906  bnj594  33067
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