Theorem nfnae 1702

Description: All variables are effectively bound in a distinct variable specifier. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfnae	⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Proof of Theorem nfnae

Step	Hyp	Ref	Expression
1		nfae 1699	. 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦
2	1	nfn 1638	1 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦

Syntax hints:  ¬ wn 3  ∀wal 1333  Ⅎwnf 1440

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 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-fal 1341  df-nf 1441

This theorem is referenced by:  sbequ6  1763  dvelimfv  1991  nfsb4t  1994