Theorem nfcri

Description: Consequence of the not-free predicate. (Note that unlike nfcr , this does not require y and A to be disjoint.) (Contributed by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypothesis	nfcri.1	⊢ Ⅎ 𝑥 𝐴
Assertion	nfcri	⊢ Ⅎ 𝑥 𝑦 ∈ 𝐴

Proof

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