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Theorem nndc 11307
Description: Double negation of decidability of a formula. Intuitionistic logic refutes undecidability (but, of course, 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 11306 . 2  |-  -.  -.  ( ph  \/  -.  ph )
2 df-dc 781 . . 3  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
32notbii 629 . 2  |-  ( -. DECID  ph  <->  -.  ( ph  \/  -.  ph ) )
41, 3mtbir 631 1  |-  -.  -. DECID  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 664  DECID wdc 780
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  df-dc 781
This theorem is referenced by:  dcdc  11308
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