Theorem nfsn

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

	Ref	Expression
Hypothesis	nfsn.1	⊢ Ⅎ 𝑥 𝐴
Assertion	nfsn	⊢ Ⅎ 𝑥 { 𝐴 }

Proof

Step	Hyp	Ref	Expression
1		nfsn.1	⊢ Ⅎ 𝑥 𝐴
2		dfsn2	⊢ { 𝐴 } = { 𝐴 , 𝐴 }
3	1 1	nfpr	⊢ Ⅎ 𝑥 { 𝐴 , 𝐴 }
4	2 3	nfcxfr	⊢ Ⅎ 𝑥 { 𝐴 }