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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 2027 | . 2 ⊢ Ⅎx y ∈ {x ∣ φ} | |
2 | 1 | nfci 2165 | 1 ⊢ Ⅎx{x ∣ φ} |
Colors of variables: wff set class |
Syntax hints: {cab 2023 Ⅎwnfc 2162 |
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 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-nfc 2164 |
This theorem is referenced by: abid2f 2199 nfrab1 2483 elabgt 2678 elabgf 2679 nfsbc1d 2774 ss2ab 3002 abn0r 3237 euabsn 3431 iunab 3694 iinab 3709 sniota 4837 elabgft1 9252 elabgf2 9254 |
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