Definition df-stab 831

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 830	. 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  832  stabnot  833  dcstab  844  stdcndc  845  stdcndcOLD  846  stdcn  847  const  852  imanst  888  ddifstab  3268  exmid1stab  4209  2omotap  7258  bj-trst  14494  bj-fast  14496  bj-nnbist  14499  bj-stim  14501  bj-stan  14502  bj-stand  14503  bj-stal  14504  bj-pm2.18st  14505  bj-con1st  14506  bdstab  14582  subctctexmid  14753