Theorem nfci

Description: Deduce that a class A does not have x free in it. (Contributed by Mario Carneiro, 11-Aug-2016)

	Ref	Expression
Hypothesis	nfci.1	$$⊢Ⅎxy\in A$$
Assertion	nfci	$$⊢\underset{\_}{Ⅎ}xA$$

Proof

Step	Hyp	Ref	Expression
1		nfci.1	$$⊢Ⅎxy\in A$$
2		df-nfc	$$⊢\underset{\_}{Ⅎ}xA\leftrightarrow \forall yℲxy\in A$$
3	2 1	mpgbir	$$⊢\underset{\_}{Ⅎ}xA$$