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Mirrors > Home > ILE Home > Th. List > nfaba1 | GIF version |
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
nfaba1 | ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1434 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | nfab 2182 | 1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑} |
Colors of variables: wff set class |
Syntax hints: ∀wal 1241 {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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
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: nfopd 3566 nfimad 4677 nfiota1 4869 nffvd 5187 |
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