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	$$⊢\neg \forall xx=y\to Ⅎxy=z$$

Proof

Step	Hyp	Ref	Expression
1		nfeqf2	$$⊢\neg \forall xx=y\to Ⅎxz=y$$
2		equcom	$$⊢z=y\leftrightarrow y=z$$
3	2	nfbii	$$⊢Ⅎxz=y\leftrightarrow Ⅎxy=z$$
4	1 3	sylib	$$⊢\neg \forall xx=y\to Ⅎxy=z$$