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Theorem bnj170 27509
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj170  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ps  /\  ch )  /\  ph )
)

Proof of Theorem bnj170
StepHypRef Expression
1 3anrot 944 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ch  /\ 
ph ) )
2 df-3an 941 . 2  |-  ( ( ps  /\  ch  /\  ph )  <->  ( ( ps 
/\  ch )  /\  ph ) )
31, 2bitri 242 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ps  /\  ch )  /\  ph )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360    /\ w3a 939
This theorem is referenced by:  bnj543  27711  bnj605  27725  bnj594  27730  bnj607  27734  bnj908  27749  bnj1173  27818
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 941
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