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Theorem bj-stabpeirce 34003
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 ((((((𝜑𝜓) → 𝜓) → 𝜑) → 𝜓) → 𝜓) → (((𝜓𝜑) → 𝜓) → 𝜓))

Proof of Theorem bj-stabpeirce
StepHypRef Expression
1 jarr 106 . . 3 ((((𝜑𝜓) → 𝜓) → 𝜑) → (𝜓𝜑))
21imim1i 63 . 2 (((𝜓𝜑) → 𝜓) → ((((𝜑𝜓) → 𝜓) → 𝜑) → 𝜓))
32imim1i 63 1 ((((((𝜑𝜓) → 𝜓) → 𝜑) → 𝜓) → 𝜓) → (((𝜓𝜑) → 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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