Theorem nfnae 1956

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 1954	. 2 ⊢ Ⅎz∀x x = y
2	1	nfn 1793	1 ⊢ Ⅎz ¬ ∀x x = y

Syntax hints:  ¬ wn 3  ∀wal 1540  Ⅎwnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  nfeqf  1958  exdistrf  1971  nfald2  1972  equs5  1996  dvelimf  1997  sbequ6  2032  nfsb2  2058  nfsb4t  2080  dvelimdf  2082  sbco2  2086  sbco3  2088  sbcom  2089  sb9i  2094  sbal2  2134  nfeud2  2216  nfabd2  2508  ralcom2  2776  copsexg  4608  dfid3  4769