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	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → Ⅎ 𝑥 𝑦 = 𝑧 )

Proof

Step	Hyp	Ref	Expression
1		nfeqf2	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → Ⅎ 𝑥 𝑧 = 𝑦 )
2		equcom	⊢ ( 𝑧 = 𝑦 ↔ 𝑦 = 𝑧 )
3	2	nfbii	⊢ ( Ⅎ 𝑥 𝑧 = 𝑦 ↔ Ⅎ 𝑥 𝑦 = 𝑧 )
4	1 3	sylib	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → Ⅎ 𝑥 𝑦 = 𝑧 )