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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 2129 | . 2 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} → ∀𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}) | |
2 | 1 | nfi 1439 | 1 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1437 ∈ wcel 1481 {cab 2126 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 |
This theorem is referenced by: abbi 2254 nfab1 2284 ralab2 2852 rexab2 2854 abn0m 3393 rabn0m 3395 eluniab 3756 elintab 3790 intexabim 4085 iinexgm 4087 opabex3d 6027 opabex3 6028 |
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