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Mirrors > Home > ILE Home > Th. List > nfab1 | GIF version |
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfab1 | ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfsab1 2030 | . 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} | |
2 | 1 | nfci 2168 | 1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: {cab 2026 Ⅎwnfc 2165 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-nfc 2167 |
This theorem is referenced by: abid2f 2202 nfrab1 2489 elabgt 2684 elabgf 2685 nfsbc1d 2780 ss2ab 3008 abn0r 3243 euabsn 3440 iunab 3703 iinab 3718 sniota 4894 elabgft1 9917 elabgf2 9919 |
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