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Theorem bj-pm2.18st 12947
Description: Clavius law for stable formulas. See pm2.18dc 840. (Contributed by BJ, 4-Dec-2023.)
Assertion
Ref Expression
bj-pm2.18st (STAB 𝜑 → ((¬ 𝜑𝜑) → 𝜑))

Proof of Theorem bj-pm2.18st
StepHypRef Expression
1 df-stab 816 . 2 (STAB 𝜑 ↔ (¬ ¬ 𝜑𝜑))
2 bj-nnclavius 12939 . . 3 ((¬ 𝜑𝜑) → ¬ ¬ 𝜑)
32imim1i 60 . 2 ((¬ ¬ 𝜑𝜑) → ((¬ 𝜑𝜑) → 𝜑))
41, 3sylbi 120 1 (STAB 𝜑 → ((¬ 𝜑𝜑) → 𝜑))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  STAB wstab 815
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in1 603  ax-in2 604
This theorem depends on definitions:  df-bi 116  df-stab 816
This theorem is referenced by: (None)
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