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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 2107 | . 2 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} | |
2 | 1 | nfci 2248 | 1 ⊢ Ⅎ𝑥{𝑥 ∣ 𝜑} |
Colors of variables: wff set class |
Syntax hints: {cab 2103 Ⅎwnfc 2245 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-nfc 2247 |
This theorem is referenced by: abid2f 2283 nfrab1 2587 elabgt 2799 elabgf 2800 nfsbc1d 2898 ss2ab 3135 abn0r 3357 euabsn 3563 iunab 3829 iinab 3844 sniota 5085 nfixp1 6580 elabgft1 12912 elabgf2 12914 |
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