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Mirrors > Home > ILE Home > Th. List > df-stab | GIF version |
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.) |
Ref | Expression |
---|---|
df-stab | ⊢ (STAB 𝜑 ↔ (¬ ¬ 𝜑 → 𝜑)) |
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)) |
Colors of variables: wff set class |
This definition is referenced by: stbid 832 stabnot 833 dcstab 844 stdcndc 845 stdcndcOLD 846 stdcn 847 const 852 imanst 888 ddifstab 3267 exmid1stab 4208 2omotap 7257 bj-trst 14461 bj-fast 14463 bj-nnbist 14466 bj-stim 14468 bj-stan 14469 bj-stand 14470 bj-stal 14471 bj-pm2.18st 14472 bj-con1st 14473 bdstab 14549 subctctexmid 14720 |
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