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Theorem bnj251 28967
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj251  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\  ( ps  /\  ( ch  /\  th ) ) ) )

Proof of Theorem bnj251
StepHypRef Expression
1 bnj250 28966 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\  ( ( ps  /\  ch )  /\  th )
) )
2 anass 631 . . 3  |-  ( ( ( ps  /\  ch )  /\  th )  <->  ( ps  /\  ( ch  /\  th ) ) )
32anbi2i 676 . 2  |-  ( (
ph  /\  ( ( ps  /\  ch )  /\  th ) )  <->  ( ph  /\  ( ps  /\  ( ch  /\  th ) ) ) )
41, 3bitri 241 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\  ( ps  /\  ( ch  /\  th ) ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    /\ w-bnj17 28951
This theorem is referenced by:  bnj255  28970  bnj535  29162  bnj570  29177  bnj953  29211  bnj1110  29252
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 28952
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