Theorem nfrel

Description: Bound-variable hypothesis builder for a relation. (Contributed by NM, 31-Jan-2004) (Revised by Mario Carneiro, 15-Oct-2016)

	Ref	Expression
Hypothesis	nfrel.1	$$⊢\underset{\_}{Ⅎ}xA$$
Assertion	nfrel	$$⊢Ⅎx\mathrm{Rel}A$$

Proof

Step	Hyp	Ref	Expression
1		nfrel.1	$$⊢\underset{\_}{Ⅎ}xA$$
2		df-rel	$$⊢\mathrm{Rel}A\leftrightarrow A\subseteq \mathrm{V}\times \mathrm{V}$$
3		nfcv	$$⊢\underset{\_}{Ⅎ}x\left(\mathrm{V}\times \mathrm{V}\right)$$
4	1 3	nfss	$$⊢ℲxA\subseteq \mathrm{V}\times \mathrm{V}$$
5	2 4	nfxfr	$$⊢Ⅎx\mathrm{Rel}A$$