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 used by:  stbid  844  stabnot  845  dcstab  856  stdcndc  857  stdcndcOLD  858  stdcn  859  const  864  imanst  900  ddifstab  3361  exmid1stab  4345  fvdifsuppst  6484  suppssrst  6501  suppssrgst  6502  2omotap  7625  bj-trst  16779  bj-fast  16781  bj-nnbist  16784  bj-stim  16786  bj-stan  16787  bj-stand  16788  bj-stal  16789  bj-pm2.18st  16790  bj-con1st  16791  bdstab  16865  subctctexmid  17042  exmidnotnotr  17048