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Mirrors > Home > ILE Home > Th. List > stabnot | GIF version |
Description: Every negated formula is stable. (Contributed by David A. Wheeler, 13-Aug-2018.) |
Ref | Expression |
---|---|
stabnot | ⊢ STAB ¬ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnotnot 629 | . . 3 ⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑) | |
2 | 1 | biimpi 119 | . 2 ⊢ (¬ ¬ ¬ 𝜑 → ¬ 𝜑) |
3 | df-stab 826 | . 2 ⊢ (STAB ¬ 𝜑 ↔ (¬ ¬ ¬ 𝜑 → ¬ 𝜑)) | |
4 | 2, 3 | mpbir 145 | 1 ⊢ STAB ¬ 𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 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 ax-in1 609 ax-in2 610 |
This theorem depends on definitions: df-bi 116 df-stab 826 |
This theorem is referenced by: dcnn 843 cnstab 8551 |
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