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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-stabpeirce | Structured version Visualization version GIF version |
Description: Over minimal implicational calculus, Peirce's law is implied by the (classical refutation equivalent of) the double negation of the stability of any proposition. (Contributed by BJ, 30-Nov-2023.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-stabpeirce | ⊢ ((((((𝜑 → 𝜓) → 𝜓) → 𝜑) → 𝜓) → 𝜓) → (((𝜓 → 𝜑) → 𝜓) → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jarr 106 | . . 3 ⊢ ((((𝜑 → 𝜓) → 𝜓) → 𝜑) → (𝜓 → 𝜑)) | |
2 | 1 | imim1i 63 | . 2 ⊢ (((𝜓 → 𝜑) → 𝜓) → ((((𝜑 → 𝜓) → 𝜓) → 𝜑) → 𝜓)) |
3 | 2 | imim1i 63 | 1 ⊢ ((((((𝜑 → 𝜓) → 𝜓) → 𝜑) → 𝜓) → 𝜓) → (((𝜓 → 𝜑) → 𝜓) → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: (None) |
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