Theorem nfcrii

Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016) Avoid ax-10 , ax-11 . (Revised by GG, 23-May-2024)

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

Proof

Step	Hyp	Ref	Expression
1		nfcrii.1	⊢ Ⅎ 𝑥 𝐴
2	1	nfcri	⊢ Ⅎ 𝑥 𝑦 ∈ 𝐴
3	2	nf5ri	⊢ ( 𝑦 ∈ 𝐴 → ∀ 𝑥 𝑦 ∈ 𝐴 )