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Mirrors > Home > ILE Home > Th. List > nfnae | GIF version |
Description: All variables are effectively bound in a distinct variable specifier. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfnae | ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfae 1697 | . 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦 | |
2 | 1 | nfn 1636 | 1 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∀wal 1329 Ⅎwnf 1436 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 |
This theorem is referenced by: sbequ6 1756 dvelimfv 1986 nfsb4t 1989 |
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