Theorem nfcrd

Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016)

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

Proof

Step	Hyp	Ref	Expression
1		nfcrd.1	$$⊢\phi \to \underset{\_}{Ⅎ}xA$$
2		nfcr	$$⊢\underset{\_}{Ⅎ}xA\to Ⅎxy\in A$$
3	1 2	syl	$$⊢\phi \to Ⅎxy\in A$$