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Theorem bnj256 29168
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 29162 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( (
( ph  /\  ps )  /\  ch )  /\  th ) )
2 anass 632 . 2  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )
) )
31, 2bitri 242 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps )  /\  ( ch  /\  th )
) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360    /\ w-bnj17 29148
This theorem is referenced by:  bnj257  29169  bnj432  29178  bnj543  29362  bnj546  29365  bnj557  29370  bnj916  29402  bnj969  29415  bnj1090  29446  bnj1118  29451  bnj1174  29470
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 179  df-an 362  df-3an 939  df-bnj17 29149
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