Theorem nfcrii

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

	Ref	Expression
Hypothesis	nfcrii.1	$$⊢\underset{\_}{Ⅎ}xA$$
Assertion	nfcrii	$$⊢y\in A\to \forall xy\in A$$

Proof

Step	Hyp	Ref	Expression
1		nfcrii.1	$$⊢\underset{\_}{Ⅎ}xA$$
2	1	nfcri	$$⊢Ⅎxy\in A$$
3	2	nf5ri	$$⊢y\in A\to \forall xy\in A$$