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Theorem an31 775
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 774 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  <->  ( ch  /\  ( ps  /\  ph ) ) )
2 anass 630 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ph  /\  ( ps  /\  ch ) ) )
3 anass 630 . 2  |-  ( ( ( ch  /\  ps )  /\  ph )  <->  ( ch  /\  ( ps  /\  ph ) ) )
41, 2, 33bitr4i 268 1  |-  ( ( ( ph  /\  ps )  /\  ch )  <->  ( ( ch  /\  ps )  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358
This theorem is referenced by:  euind  2952  reuind  2968  dchrelbas3  20477  lhpexle3  30201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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