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Theorem an31 553
Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)
Assertion
Ref Expression
an31  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ch  /\  ps )  /\  ph ) )

Proof of Theorem an31
StepHypRef Expression
1 an13 552 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  <->  ( ch  /\  ( ps  /\  ph ) ) )
2 anass 398 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ph  /\  ( ps  /\  ch ) ) )
3 anass 398 . 2  |-  ( ( ( ch  /\  ps )  /\  ph )  <->  ( ch  /\  ( ps  /\  ph ) ) )
41, 2, 33bitr4i 211 1  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ch  /\  ps )  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  euind  2871  reuind  2889
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