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Mirrors > Home > ILE Home > Th. List > nfsab1 | GIF version |
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfsab1 | ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbab1 2078 | . 2 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} → ∀𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}) | |
2 | 1 | nfi 1397 | 1 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1395 ∈ wcel 1439 {cab 2075 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 |
This theorem is referenced by: abbi 2202 nfab1 2231 ralab2 2780 rexab2 2782 abn0m 3312 rabn0m 3314 eluniab 3671 elintab 3705 intexabim 3994 iinexgm 3996 opabex3d 5906 opabex3 5907 |
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