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Theorem nbior 856
Description: If two propositions are not equivalent, then at least one is true. (Contributed by BJ, 19-Apr-2019.)
Assertion
Ref Expression
nbior  |-  ( -.  ( ph  <->  ps )  ->  ( ph  \/  ps ) )

Proof of Theorem nbior
StepHypRef Expression
1 pm5.21 854 . . 3  |-  ( ( -.  ph  /\  -.  ps )  ->  ( ph  <->  ps )
)
21con3i 135 . 2  |-  ( -.  ( ph  <->  ps )  ->  -.  ( -.  ph  /\ 
-.  ps ) )
3 oran 496 . 2  |-  ( (
ph  \/  ps )  <->  -.  ( -.  ph  /\  -.  ps ) )
42, 3sylibr 212 1  |-  ( -.  ( ph  <->  ps )  ->  ( ph  \/  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    \/ wo 368    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371
This theorem is referenced by: (None)
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