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Theorem nnexmid 11317
Description: Double negation of excluded middle. Intuitionistic logic refutes the negation of excluded middle (but, of course, does not prove excluded middle) for any formula. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
nnexmid  |-  -.  -.  ( ph  \/  -.  ph )

Proof of Theorem nnexmid
StepHypRef Expression
1 pm3.24 662 . 2  |-  -.  ( -.  ph  /\  -.  -.  ph )
2 ioran 704 . 2  |-  ( -.  ( ph  \/  -.  ph )  <->  ( -.  ph  /\ 
-.  -.  ph ) )
31, 2mtbir 631 1  |-  -.  -.  ( ph  \/  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 102    \/ wo 664
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  nndc  11318
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