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	$$⊢y\in A\to \forall xy\in A$$
Assertion	nfcii	$$⊢\underset{\_}{Ⅎ}xA$$

Proof

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