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Theorem bnj256 34178
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj256  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )
) )

Proof of Theorem bnj256
StepHypRef Expression
1 bnj248 34172 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( (
( ph  /\  ps )  /\  ch )  /\  th ) )
2 anass 647 . 2  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )
) )
31, 2bitri 249 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )
) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 367    /\ w-bnj17 34158
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 369  df-3an 973  df-bnj17 34159
This theorem is referenced by:  bnj257  34179  bnj432  34188  bnj543  34371  bnj546  34374  bnj557  34379  bnj916  34411  bnj969  34424  bnj1090  34455  bnj1118  34460  bnj1174  34479
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