Definition df-stab 833

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 832	. 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  834  stabnot  835  dcstab  846  stdcndc  847  stdcndcOLD  848  stdcn  849  const  854  imanst  890  ddifstab  3307  exmid1stab  4257  2omotap  7384  bj-trst  15789  bj-fast  15791  bj-nnbist  15794  bj-stim  15796  bj-stan  15797  bj-stand  15798  bj-stal  15799  bj-pm2.18st  15800  bj-con1st  15801  bdstab  15877  subctctexmid  16052