Theorem nfcii

Description: Deduce that a class A does not have x free in it. (Contributed by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypothesis	nfcii.1	⊢ ( 𝑦 ∈ 𝐴 → ∀ 𝑥 𝑦 ∈ 𝐴 )
Assertion	nfcii	⊢ Ⅎ 𝑥 𝐴

Proof

Step	Hyp	Ref	Expression
1		nfcii.1	⊢ ( 𝑦 ∈ 𝐴 → ∀ 𝑥 𝑦 ∈ 𝐴 )
2	1	nf5i	⊢ Ⅎ 𝑥 𝑦 ∈ 𝐴
3	2	nfci	⊢ Ⅎ 𝑥 𝐴