Definition df-stab 838

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 837	. 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  839  stabnot  840  dcstab  851  stdcndc  852  stdcndcOLD  853  stdcn  854  const  859  imanst  895  ddifstab  3339  exmid1stab  4298  2omotap  7478  bj-trst  16356  bj-fast  16358  bj-nnbist  16361  bj-stim  16363  bj-stan  16364  bj-stand  16365  bj-stal  16366  bj-pm2.18st  16367  bj-con1st  16368  bdstab  16443  subctctexmid  16622