Definition df-stab 816

Description: Propositions where a double-negative can be removed are called stable. See Chapter 2 [Moschovakis] p. 2.

Our notation for stability is a connective STAB which we place before the formula in question. For example, STAB 𝑥 = 𝑦 corresponds to "𝑥 = 𝑦 is stable".

(Contributed by David A. Wheeler, 13-Aug-2018.)

Assertion

Ref	Expression
df-stab	⊢ (STAB 𝜑 ↔ (¬ ¬ 𝜑 → 𝜑))

Detailed syntax breakdown of Definition df-stab

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2	1	wstab 815	. 2 wff STAB 𝜑
3	1	wn 3	. . . 4 wff ¬ 𝜑
4	3	wn 3	. . 3 wff ¬ ¬ 𝜑
5	4, 1	wi 4	. 2 wff (¬ ¬ 𝜑 → 𝜑)
6	2, 5	wb 104	1 wff (STAB 𝜑 ↔ (¬ ¬ 𝜑 → 𝜑))

This definition is referenced by:  stbid  817  stabnot  818  dcstab  829  stdcndc  830  stdcndcOLD  831  stdcn  832  const  837  imanst  873  ddifstab  3203  cnstab  8400  bj-trst  12940  bj-fast  12941  bj-nnbist  12942  bj-stim  12943  bj-stan  12944  bj-stand  12945  bj-stal  12946  bj-pm2.18st  12947  bdstab  13014  exmid1stab  13184  subctctexmid  13185