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Theorem nnexmid 10286
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 pm3.24 637 . 2  |-  -.  ( -.  ph  /\  -.  -.  ph )
2 ioran 679 . 2  |-  ( -.  ( ph  \/  -.  ph )  <->  ( -.  ph  /\ 
-.  -.  ph ) )
31, 2mtbir 606 1  |-  -.  -.  ( ph  \/  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 101    \/ wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  nndc  10287
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