Theorem nfwe

Description: Bound-variable hypothesis builder for well-orderings. (Contributed by Stefan O'Rear, 20-Jan-2015) (Revised by Mario Carneiro, 14-Oct-2016)

	Ref	Expression
Hypotheses	nffr.r	$$⊢\underset{\_}{Ⅎ}xR$$
	nffr.a	$$⊢\underset{\_}{Ⅎ}xA$$
Assertion	nfwe	$$⊢ℲxR\mathrm{We}A$$

Proof

Step	Hyp	Ref	Expression
1		nffr.r	$$⊢\underset{\_}{Ⅎ}xR$$
2		nffr.a	$$⊢\underset{\_}{Ⅎ}xA$$
3		df-we	$$⊢R\mathrm{We}A\leftrightarrow \left(R\mathrm{Fr}A\wedge R\mathrm{Or}A\right)$$
4	1 2	nffr	$$⊢ℲxR\mathrm{Fr}A$$
5	1 2	nfso	$$⊢ℲxR\mathrm{Or}A$$
6	4 5	nfan	$$⊢Ⅎx\left(R\mathrm{Fr}A\wedge R\mathrm{Or}A\right)$$
7	3 6	nfxfr	$$⊢ℲxR\mathrm{We}A$$