Theorem nfeqf1 2000

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 1998	. 2 |- ( -. A. x x = y -> F/ x z = y )
2		equcom 1734	. . 3 |- ( z = y <-> y = z )
3	2	nfbii 1615	. 2 |- ( F/ x z = y <-> F/ x y = z )
4	1, 3	sylib 196	1 |- ( -. A. x x = y -> F/ x y = z )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1368   F/wnf 1590

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794  ax-13 1952

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591

This theorem is referenced by:  dveeq1  2001  sbal2  2180  nfeud2  2275  wl-mo2dnae  28535