Definition df-stab 843

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 842	. 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  844  stabnot  845  dcstab  856  stdcndc  857  stdcndcOLD  858  stdcn  859  const  864  imanst  900  ddifstab  3361  exmid1stab  4343  fvdifsuppst  6478  suppssrst  6495  suppssrgst  6496  2omotap  7619  bj-trst  16750  bj-fast  16752  bj-nnbist  16755  bj-stim  16757  bj-stan  16758  bj-stand  16759  bj-stal  16760  bj-pm2.18st  16761  bj-con1st  16762  bdstab  16836  subctctexmid  17013  exmidnotnotr  17018