Theorem stabnot 834

Description: Every negated formula is stable. (Contributed by David A. Wheeler, 13-Aug-2018.)

Assertion

Ref	Expression
stabnot	⊢ STAB ¬ 𝜑

Proof of Theorem stabnot

Step	Hyp	Ref	Expression
1		notnotnot 635	. . 3 ⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)
2	1	biimpi 120	. 2 ⊢ (¬ ¬ ¬ 𝜑 → ¬ 𝜑)
3		df-stab 832	. 2 ⊢ (STAB ¬ 𝜑 ↔ (¬ ¬ ¬ 𝜑 → ¬ 𝜑))
4	2, 3	mpbir 146	1 ⊢ STAB ¬ 𝜑

Syntax hints:  ¬ wn 3   → wi 4  STAB wstab 831

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117  df-stab 832

This theorem is referenced by:  dcnn  849  cnstab  8620