Theorem nfae 1742

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 1741	. 2 |- ( A. x x = y -> A. z A. x x = y )
2	1	nfi 1485	1 |- F/ z A. x x = y

Syntax hints:   A.wal 1371   F/wnf 1483

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-nf 1484

This theorem is referenced by:  nfnae  1745  sbequ5  1805  a16nf  1889  dvelimfv  2039  dvelimor  2046  copsexg  4288