Theorem bj-stabpeirce 33913

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.)

Assertion

Ref	Expression
bj-stabpeirce	⊢ ((((((𝜑 → 𝜓) → 𝜓) → 𝜑) → 𝜓) → 𝜓) → (((𝜓 → 𝜑) → 𝜓) → 𝜓))

Proof of Theorem bj-stabpeirce

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))

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)