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Theorem bibif 335
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 334 . 2  |-  ( -. 
ps  ->  ( -.  ph  <->  ( ps  <->  ph ) ) )
2 bicom 191 . 2  |-  ( ( ps  <->  ph )  <->  ( ph  <->  ps ) )
31, 2syl6rbb 253 1  |-  ( -. 
ps  ->  ( ( ph  <->  ps )  <->  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176
This theorem is referenced by:  nbn  336
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
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