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Theorem nndc 819
Description: Double negation of decidability of a formula. Intuitionistic logic refutes undecidability (but does not prove decidability) of any formula. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
nndc  |-  -.  -. DECID  ph

Proof of Theorem nndc
StepHypRef Expression
1 nnexmid 818 . 2  |-  -.  -.  ( ph  \/  -.  ph )
2 df-dc 803 . . 3  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
32notbii 640 . 2  |-  ( -. DECID  ph  <->  -.  ( ph  \/  -.  ph ) )
41, 3mtbir 643 1  |-  -.  -. DECID  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 680  DECID wdc 802
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 586  ax-in2 587  ax-io 681
This theorem depends on definitions:  df-bi 116  df-dc 803
This theorem is referenced by:  bj-nnst  12798  bj-dcdc  12799  bj-stdc  12800
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