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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 2105 | . 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} | |
2 | 1 | nfci 2245 | 1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: {cab 2101 Ⅎwnfc 2242 |
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 1406 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-11 1467 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 |
This theorem depends on definitions: df-bi 116 df-nf 1420 df-sb 1719 df-clab 2102 df-nfc 2244 |
This theorem is referenced by: abid2f 2280 nfrab1 2584 elabgt 2795 elabgf 2796 nfsbc1d 2894 ss2ab 3131 abn0r 3353 euabsn 3559 iunab 3825 iinab 3840 sniota 5073 nfixp1 6566 elabgft1 12677 elabgf2 12679 |
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