Theorem nfsn

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

	Ref	Expression
Hypothesis	nfsn.1	$$⊢\underset{\_}{Ⅎ}xA$$
Assertion	nfsn	$$⊢\underset{\_}{Ⅎ}x\left\{A\right\}$$

Proof

Step	Hyp	Ref	Expression
1		nfsn.1	$$⊢\underset{\_}{Ⅎ}xA$$
2		dfsn2	$$⊢\left\{A\right\}=\left\{A,A\right\}$$
3	1 1	nfpr	$$⊢\underset{\_}{Ⅎ}x\left\{A,A\right\}$$
4	2 3	nfcxfr	$$⊢\underset{\_}{Ⅎ}x\left\{A\right\}$$