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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-nnst | GIF version |
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.) |
Ref | Expression |
---|---|
bj-nnst | ⊢ ¬ ¬ STAB 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nndc 837 | . 2 ⊢ ¬ ¬ DECID 𝜑 | |
2 | dcstab 830 | . . 3 ⊢ (DECID 𝜑 → STAB 𝜑) | |
3 | 2 | con3i 622 | . 2 ⊢ (¬ STAB 𝜑 → ¬ DECID 𝜑) |
4 | 1, 3 | mto 652 | 1 ⊢ ¬ ¬ STAB 𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 STAB wstab 816 DECID wdc 820 |
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 df-stab 817 df-dc 821 |
This theorem is referenced by: bj-dcst 13138 bj-stst 13139 |
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