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Theorem bnj170 27990
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 941 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ps  /\  ch  /\ 
ph ) )
2 df-3an 938 . 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 936
This theorem is referenced by:  bnj543  28192  bnj605  28206  bnj594  28211  bnj607  28215  bnj908  28230  bnj1173  28299
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 938
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