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Description: If a formula is not refutable, then it is stable if and only if it is provable. By double-negation translation, if is a classical tautology, then is an intuitionistic tautology. Therefore, if is a classical tautology, then is intuitionistically equivalent to its stability (and to its decidability, see bj-nnbidc 13751). (Contributed by BJ, 24-Nov-2023.) |
Ref | Expression |
---|---|
bj-nnbist | STAB |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-stab 826 | . . . 4 STAB | |
2 | 1 | biimpi 119 | . . 3 STAB |
3 | 2 | com12 30 | . 2 STAB |
4 | bj-trst 13733 | . 2 STAB | |
5 | 3, 4 | impbid1 141 | 1 STAB |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 STAB wstab 825 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-stab 826 |
This theorem is referenced by: bj-stst 13739 bj-nnbidc 13751 bj-stdc 13754 |
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