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Theorem an13 505
Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)
Assertion
Ref Expression
an13  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  <->  ( ch  /\  ( ps  /\  ph ) ) )

Proof of Theorem an13
StepHypRef Expression
1 an12 503 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  <->  ( ps  /\  ( ph  /\  ch ) ) )
2 anass 387 . 2  |-  ( ( ( ps  /\  ph )  /\  ch )  <->  ( ps  /\  ( ph  /\  ch ) ) )
3 ancom 257 . 2  |-  ( ( ( ps  /\  ph )  /\  ch )  <->  ( ch  /\  ( ps  /\  ph ) ) )
41, 2, 33bitr2i 201 1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  <->  ( ch  /\  ( ps  /\  ph ) ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 101    <-> wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  an31  506  elxp2  4391
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