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Mirrors > Home > ILE Home > Th. List > nfae | GIF version |
Description: All variables are effectively bound in an identical variable specifier. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfae | ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbae 1711 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦) | |
2 | 1 | nfi 1455 | 1 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦 |
Colors of variables: wff set class |
Syntax hints: ∀wal 1346 Ⅎwnf 1453 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 |
This theorem depends on definitions: df-bi 116 df-nf 1454 |
This theorem is referenced by: nfnae 1715 sbequ5 1775 a16nf 1859 dvelimfv 2004 dvelimor 2011 copsexg 4229 |
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