Theorem wl-ax11-lem7

Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019)

	Ref	Expression
Assertion	wl-ax11-lem7	⊢ ( ∀ 𝑥 ( ¬ ∀ 𝑥 𝑥 = 𝑦 ∧ 𝜑 ) ↔ ( ¬ ∀ 𝑥 𝑥 = 𝑦 ∧ ∀ 𝑥 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		nfna1	⊢ Ⅎ 𝑥 ¬ ∀ 𝑥 𝑥 = 𝑦
2	1	19.28	⊢ ( ∀ 𝑥 ( ¬ ∀ 𝑥 𝑥 = 𝑦 ∧ 𝜑 ) ↔ ( ¬ ∀ 𝑥 𝑥 = 𝑦 ∧ ∀ 𝑥 𝜑 ) )