Metamath Proof Explorer


Theorem nfsn

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

Ref Expression
Hypothesis nfsn.1
|- F/_ x A
Assertion nfsn
|- F/_ x { A }

Proof

Step Hyp Ref Expression
1 nfsn.1
 |-  F/_ x A
2 dfsn2
 |-  { A } = { A , A }
3 1 1 nfpr
 |-  F/_ x { A , A }
4 2 3 nfcxfr
 |-  F/_ x { A }