Theorem nfeqf1 2150

Description: An equation between setvar is free of any other setvar. (Contributed by Wolf Lammen, 10-Jun-2019.)

Assertion

Ref	Expression
nfeqf1	|- ( -. A. x x = y -> F/ x y = z )

Distinct variable group:   x, z

Proof of Theorem nfeqf1

Step	Hyp	Ref	Expression
1		nfeqf2 2148	. 2 |- ( -. A. x x = y -> F/ x z = y )
2		equcom 1870	. . 3 |- ( z = y <-> y = z )
3	2	nfbii 1703	. 2 |- ( F/ x z = y <-> F/ x y = z )
4	1, 3	sylib 201	1 |- ( -. A. x x = y -> F/ x y = z )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1450   F/wnf 1675

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104

This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676

This theorem is referenced by:  dveeq1  2151  sbal2  2310  nfeud2  2331  wl-mo2df  31969  wl-eudf  31971