Definition df-stab 832

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 831	. 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 105	1 wff (STAB 𝜑 ↔ (¬ ¬ 𝜑 → 𝜑))

This definition is referenced by:  stbid  833  stabnot  834  dcstab  845  stdcndc  846  stdcndcOLD  847  stdcn  848  const  853  imanst  889  ddifstab  3292  exmid1stab  4238  2omotap  7321  bj-trst  15301  bj-fast  15303  bj-nnbist  15306  bj-stim  15308  bj-stan  15309  bj-stand  15310  bj-stal  15311  bj-pm2.18st  15312  bj-con1st  15313  bdstab  15389  subctctexmid  15561