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Theorem bj-nnst 13023
Description: Double negation of stability of a formula. Intuitionistic logic refutes unstability (but does not prove stability) of any formula. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
bj-nnst ¬ ¬ STAB 𝜑

Proof of Theorem bj-nnst
StepHypRef Expression
1 nndc 836 . 2 ¬ ¬ DECID 𝜑
2 dcstab 829 . . 3 (DECID 𝜑STAB 𝜑)
32con3i 621 . 2 STAB 𝜑 → ¬ DECID 𝜑)
41, 3mto 651 1 ¬ ¬ STAB 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  STAB wstab 815  DECID wdc 819
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 603  ax-in2 604  ax-io 698
This theorem depends on definitions:  df-bi 116  df-stab 816  df-dc 820
This theorem is referenced by:  bj-dcst  13026  bj-stst  13027
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