Definition df-stab 817

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 816	. 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  818  stabnot  819  dcstab  830  stdcndc  831  stdcndcOLD  832  stdcn  833  const  838  imanst  874  ddifstab  3213  cnstab  8431  bj-trst  13122  bj-fast  13123  bj-nnbist  13124  bj-stim  13125  bj-stan  13126  bj-stand  13127  bj-stal  13128  bj-pm2.18st  13129  bdstab  13196  exmid1stab  13368  subctctexmid  13369