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Metamath Proof Explorer

Theorem nfrecs

Description: Bound-variable hypothesis builder for recs . (Contributed by Stefan O'Rear, 18-Jan-2015)

		Ref	Expression
	Hypothesis	nfrecs.f	$⊢ \underline{Ⅎ} x F$
	Assertion	nfrecs	$⊢ \underline{Ⅎ} x recs (F)$

Step	Hyp	Ref	Expression
1		nfrecs.f	$⊢ \underline{Ⅎ} x F$
2		df-recs	$⊢ recs (F) = wrecs (E, On, F)$
3		nfcv	$⊢ \underline{Ⅎ} x E$
4		nfcv	$⊢ \underline{Ⅎ} x On$
5	3 4 1	nfwrecs	$⊢ \underline{Ⅎ} x wrecs (E, On, F)$
6	2 5	nfcxfr	$⊢ \underline{Ⅎ} x recs (F)$