Theorem nfae 1647

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

Assertion

Ref	Expression
nfae	|- F/ z A. x x = y

Proof of Theorem nfae

Step	Hyp	Ref	Expression
1		hbae 1646	. 2 |- ( A. x x = y -> A. z A. x x = y )
2	1	nfi 1391	1 |- F/ z A. x x = y

Syntax hints:   A.wal 1282   F/wnf 1389

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390

This theorem is referenced by:  nfnae  1650  sbequ5  1705  a16nf  1787  dvelimfv  1928  dvelimor  1935  copsexg  3999