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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 1486 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | nfab 2240 | 1 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥𝜑} |
Colors of variables: wff set class |
Syntax hints: ∀wal 1294 {cab 2081 Ⅎwnfc 2222 |
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-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 |
This theorem depends on definitions: df-bi 116 df-nf 1402 df-sb 1700 df-clab 2082 df-nfc 2224 |
This theorem is referenced by: nfopd 3661 nfimad 4816 nfiota1 5016 nffvd 5352 |
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