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Theorem bnj256 32838
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 32832 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( (
( ph  /\  ps )  /\  ch )  /\  th ) )
2 anass 649 . 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 369    /\ w-bnj17 32818
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 32819
This theorem is referenced by:  bnj257  32839  bnj432  32848  bnj543  33030  bnj546  33033  bnj557  33038  bnj916  33070  bnj969  33083  bnj1090  33114  bnj1118  33119  bnj1174  33138
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