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Theorem bnj255 28970
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj255  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ps  /\  ( ch  /\ 
th ) ) )

Proof of Theorem bnj255
StepHypRef Expression
1 bnj251 28967 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\  ( ps  /\  ( ch  /\  th ) ) ) )
2 3anass 940 . 2  |-  ( (
ph  /\  ps  /\  ( ch  /\  th ) )  <-> 
( ph  /\  ( ps  /\  ( ch  /\  th ) ) ) )
31, 2bitr4i 244 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ps  /\  ( ch  /\ 
th ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    /\ w3a 936    /\ w-bnj17 28951
This theorem is referenced by:  bnj964  29215  bnj998  29228  bnj1033  29239  bnj1175  29274
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
  Copyright terms: Public domain W3C validator