Theorem nfsn 3452

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

Hypothesis

Ref	Expression
nfsn.1	|- F/_ x A

Assertion

Ref	Expression
nfsn	|- F/_ x { A }

Proof of Theorem nfsn

Step	Hyp	Ref	Expression
1		dfsn2 3412	. 2 |- { A } = { A , A }
2		nfsn.1	. . 3 |- F/_ x A
3	2, 2	nfpr 3442	. 2 |- F/_ x { A , A }
4	1, 3	nfcxfr 2216	1 |- F/_ x { A }

Syntax hints:   F/_wnfc 2206   {csn 3398   {cpr 3399

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-un 2977  df-sn 3404  df-pr 3405

This theorem is referenced by:  nfop  3586  nfsuc  4163  sniota  4914  dfmpt2  5864