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Theorem bnj248 29001
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj248  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( (
( ph  /\  ps )  /\  ch )  /\  th ) )

Proof of Theorem bnj248
StepHypRef Expression
1 df-bnj17 28988 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps  /\  ch )  /\  th ) )
2 df-3an 938 . . 3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
32anbi1i 677 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th ) 
<->  ( ( ( ph  /\ 
ps )  /\  ch )  /\  th ) )
41, 3bitri 241 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 28987
This theorem is referenced by:  bnj253  29005  bnj256  29007  bnj605  29215  bnj908  29239
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 28988
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