Theorem naev2

Description: Generalization of hbnaev . (Contributed by Wolf Lammen, 9-Apr-2021)

	Ref	Expression
Assertion	naev2	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑧 ¬ ∀ 𝑡 𝑡 = 𝑢 )

Proof

Step	Hyp	Ref	Expression
1		naev	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ¬ ∀ 𝑣 𝑣 = 𝑤 )
2		ax-5	⊢ ( ¬ ∀ 𝑣 𝑣 = 𝑤 → ∀ 𝑧 ¬ ∀ 𝑣 𝑣 = 𝑤 )
3		naev	⊢ ( ¬ ∀ 𝑣 𝑣 = 𝑤 → ¬ ∀ 𝑡 𝑡 = 𝑢 )
4	3	alimi	⊢ ( ∀ 𝑧 ¬ ∀ 𝑣 𝑣 = 𝑤 → ∀ 𝑧 ¬ ∀ 𝑡 𝑡 = 𝑢 )
5	1 2 4	3syl	⊢ ( ¬ ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑧 ¬ ∀ 𝑡 𝑡 = 𝑢 )