Theorem nfpr

Description: Bound-variable hypothesis builder for unordered pairs. (Contributed by NM, 14-Nov-1995)

	Ref	Expression
Hypotheses	nfpr.1	$$⊢\underset{\_}{Ⅎ}xA$$
	nfpr.2	$$⊢\underset{\_}{Ⅎ}xB$$
Assertion	nfpr	$$⊢\underset{\_}{Ⅎ}x\left\{A,B\right\}$$

Proof

Step	Hyp	Ref	Expression
1		nfpr.1	$$⊢\underset{\_}{Ⅎ}xA$$
2		nfpr.2	$$⊢\underset{\_}{Ⅎ}xB$$
3		dfpr2	$$⊢\left\{A,B\right\}=\left\{y|\left(y=A\vee y=B\right)\right\}$$
4	1	nfeq2	$$⊢Ⅎxy=A$$
5	2	nfeq2	$$⊢Ⅎxy=B$$
6	4 5	nfor	$$⊢Ⅎx\left(y=A\vee y=B\right)$$
7	6	nfab	$$⊢\underset{\_}{Ⅎ}x\left\{y|\left(y=A\vee y=B\right)\right\}$$
8	3 7	nfcxfr	$$⊢\underset{\_}{Ⅎ}x\left\{A,B\right\}$$