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Metamath Proof Explorer

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	$⊢ \underline{Ⅎ} x A$
	Assertion	nfrel	$⊢ Ⅎ x Rel A$

Step	Hyp	Ref	Expression
1		nfrel.1	$⊢ \underline{Ⅎ} x A$
2		df-rel	$⊢ Rel A \leftrightarrow A \subseteq V \times V$
3		nfcv	$⊢ \underline{Ⅎ} x (V \times V)$
4	1 3	nfss	$⊢ Ⅎ x A \subseteq V \times V$
5	2 4	nfxfr	$⊢ Ⅎ x Rel A$