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Theorem nnexmid 836
Description: Double negation of excluded middle. Intuitionistic logic refutes the negation of excluded middle (but does not prove excluded middle) for any formula. Can also be proved quickly from bj-nnor 13115 as in bj-nndcALT 13132. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
nnexmid  |-  -.  -.  ( ph  \/  -.  ph )

Proof of Theorem nnexmid
StepHypRef Expression
1 pm3.24 683 . 2  |-  -.  ( -.  ph  /\  -.  -.  ph )
2 ioran 742 . 2  |-  ( -.  ( ph  \/  -.  ph )  <->  ( -.  ph  /\ 
-.  -.  ph ) )
31, 2mtbir 661 1  |-  -.  -.  ( ph  \/  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 103    \/ wo 698
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 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  nndc  837  exmid1stab  13366
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