Theorem nfae 1699

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

Assertion

Ref	Expression
nfae	⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦

Proof of Theorem nfae

Step	Hyp	Ref	Expression
1		hbae 1698	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)
2	1	nfi 1442	1 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦

Syntax hints:  ∀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-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-nf 1441

This theorem is referenced by:  nfnae  1702  sbequ5  1762  a16nf  1846  dvelimfv  1991  dvelimor  1998  copsexg  4204