Theorem stabnot 741

Description: Every formula of the form ¬ 𝜑 is stable. Uses notnotnot 628. (Contributed by David A. Wheeler, 13-Aug-2018.)

Assertion

Ref	Expression
stabnot	⊢ STAB ¬ 𝜑

Proof of Theorem stabnot

Step	Hyp	Ref	Expression
1		notnotnot 628	. . 3 ⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)
2	1	biimpi 113	. 2 ⊢ (¬ ¬ ¬ 𝜑 → ¬ 𝜑)
3		df-stab 740	. 2 ⊢ (STAB ¬ 𝜑 ↔ (¬ ¬ ¬ 𝜑 → ¬ 𝜑))
4	2, 3	mpbir 134	1 ⊢ STAB ¬ 𝜑

Syntax hints:  ¬ wn 3   → wi 4  STAB wstab 739

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-stab 740

This theorem is referenced by: (None)