Theorem nfsn 3530

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 3488	. 2 |- { A } = { A , A }
2		nfsn.1	. . 3 |- F/_ x A
3	2, 2	nfpr 3520	. 2 |- F/_ x { A , A }
4	1, 3	nfcxfr 2237	1 |- F/_ x { A }

Syntax hints:   F/_wnfc 2227   {csn 3474   {cpr 3475

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082

This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-v 2643  df-un 3025  df-sn 3480  df-pr 3481

This theorem is referenced by:  nfop  3668  nfsuc  4268  sniota  5051  dfmpo  6050