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Theorem bnj255 33238
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 33235 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\  ( ps  /\  ( ch  /\  th ) ) ) )
2 3anass 977 . 2  |-  ( (
ph  /\  ps  /\  ( ch  /\  th ) )  <-> 
( ph  /\  ( ps  /\  ( ch  /\  th ) ) ) )
31, 2bitr4i 252 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ph  /\ 
ps  /\  ( ch  /\ 
th ) ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369    /\ w3a 973    /\ w-bnj17 33219
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 33220
This theorem is referenced by:  bnj964  33481  bnj998  33494  bnj1033  33505  bnj1175  33540
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