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Theorem bibif 688
Description: Transfer negation via an equivalence. (Contributed by NM, 3-Oct-2007.) (Proof shortened by Wolf Lammen, 28-Jan-2013.)
Assertion
Ref Expression
bibif  |-  ( -. 
ps  ->  ( ( ph  <->  ps )  <->  -.  ph ) )

Proof of Theorem bibif
StepHypRef Expression
1 nbn2 687 . 2  |-  ( -. 
ps  ->  ( -.  ph  <->  ( ps  <->  ph ) ) )
2 bicom 139 . 2  |-  ( ( ps  <->  ph )  <->  ( ph  <->  ps ) )
31, 2syl6rbb 196 1  |-  ( -. 
ps  ->  ( ( ph  <->  ps )  <->  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> 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  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  nbn  689
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