Theorem nfrecs

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

	Ref	Expression
Hypothesis	nfrecs.f	$$⊢\underset{\_}{Ⅎ}xF$$
Assertion	nfrecs	$$⊢\underset{\_}{Ⅎ}x\mathrm{recs}\left(F\right)$$

Proof

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