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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 2073 | . 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} | |
2 | 1 | nfci 2213 | 1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: {cab 2069 Ⅎwnfc 2210 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1377 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-11 1438 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 |
This theorem depends on definitions: df-bi 115 df-nf 1391 df-sb 1688 df-clab 2070 df-nfc 2212 |
This theorem is referenced by: abid2f 2247 nfrab1 2539 elabgt 2745 elabgf 2746 nfsbc1d 2842 ss2ab 3073 abn0r 3290 euabsn 3486 iunab 3750 iinab 3765 sniota 4961 elabgft1 11021 elabgf2 11023 |
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