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Theorem notbi 661
Description: Equivalence property for negation. Closed form. (Contributed by BJ, 27-Jan-2020.)
Assertion
Ref Expression
notbi  |-  ( (
ph 
<->  ps )  ->  ( -.  ph  <->  -.  ps )
)

Proof of Theorem notbi
StepHypRef Expression
1 biimpr 129 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
21con3d 626 . 2  |-  ( (
ph 
<->  ps )  ->  ( -.  ph  ->  -.  ps )
)
3 biimp 117 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
43con3d 626 . 2  |-  ( (
ph 
<->  ps )  ->  ( -.  ps  ->  -.  ph )
)
52, 4impbid 128 1  |-  ( (
ph 
<->  ps )  ->  ( -.  ph  <->  -.  ps )
)
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 609  ax-in2 610
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  notbid  662  notbii  663  ifbi  3546
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