Theorem nfeqf1 2047

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 2045	. 2 |- ( -. A. x x = y -> F/ x z = y )
2		equcom 1799	. . 3 |- ( z = y <-> y = z )
3	2	nfbii 1649	. 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 1396   F/wnf 1621

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-12 1859  ax-13 2004

This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618  df-nf 1622

This theorem is referenced by:  dveeq1  2048  sbal2  2207  nfeud2  2298  wl-mo2dnae  30259