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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-pm2.18st | GIF version |
Description: Clavius law for stable formulas. See pm2.18dc 850. (Contributed by BJ, 4-Dec-2023.) |
Ref | Expression |
---|---|
bj-pm2.18st | ⊢ (STAB 𝜑 → ((¬ 𝜑 → 𝜑) → 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-stab 826 | . 2 ⊢ (STAB 𝜑 ↔ (¬ ¬ 𝜑 → 𝜑)) | |
2 | bj-nnclavius 13772 | . . 3 ⊢ ((¬ 𝜑 → 𝜑) → ¬ ¬ 𝜑) | |
3 | 2 | imim1i 60 | . 2 ⊢ ((¬ ¬ 𝜑 → 𝜑) → ((¬ 𝜑 → 𝜑) → 𝜑)) |
4 | 1, 3 | sylbi 120 | 1 ⊢ (STAB 𝜑 → ((¬ 𝜑 → 𝜑) → 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-in1 609 ax-in2 610 |
This theorem depends on definitions: df-bi 116 df-stab 826 |
This theorem is referenced by: (None) |
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