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Theorem bnj170 31983
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 970 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ch  /\ 
ph ) )
2 df-3an 967 . 2  |-  ( ( ps  /\  ch  /\  ph )  <->  ( ( ps 
/\  ch )  /\  ph ) )
31, 2bitri 249 1  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ps  /\  ch )  /\  ph )
)
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369    /\ w3a 965
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 967
This theorem is referenced by:  bnj543  32183  bnj605  32197  bnj594  32202  bnj607  32206  bnj908  32221  bnj1173  32290
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