Theorem nfeqf1 2299

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 2297	. 2 |- ( -. A. x x = y -> F/ x z = y )
2		equcom 1945	. . 3 |- ( z = y <-> y = z )
3	2	nfbii 1778	. 2 |- ( F/ x z = y <-> F/ x y = z )
4	1, 3	sylib 208	1 |- ( -. A. x x = y -> F/ x y = z )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by:  dveeq1  2300  sbal2  2461  nfeud2  2482  nfiotad  5854  wl-mo2df  33352  wl-eudf  33354