Metamath Proof Explorer


Theorem nfeqf1

Description: An equation between setvar is free of any other setvar. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by Wolf Lammen, 10-Jun-2019) (New usage is discouraged.)

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

Proof

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