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	$$⊢\underset{\_}{Ⅎ}xA$$
Assertion	nfcri	$$⊢Ⅎxy\in A$$

Proof

Step	Hyp	Ref	Expression
1		nfcri.1	$$⊢\underset{\_}{Ⅎ}xA$$
2	1	nfcrii	$$⊢y\in A\to \forall xy\in A$$
3	2	nf5i	$$⊢Ⅎxy\in A$$