Definition df-stab 839

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 838	. 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  840  stabnot  841  dcstab  852  stdcndc  853  stdcndcOLD  854  stdcn  855  const  860  imanst  896  ddifstab  3341  exmid1stab  4304  fvdifsuppst  6422  suppssrst  6439  suppssrgst  6440  2omotap  7521  bj-trst  16437  bj-fast  16439  bj-nnbist  16442  bj-stim  16444  bj-stan  16445  bj-stand  16446  bj-stal  16447  bj-pm2.18st  16448  bj-con1st  16449  bdstab  16523  subctctexmid  16702  exmidnotnotr  16707