Theorem nfsn 3649

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 3603	. 2 |- { A } = { A , A }
2		nfsn.1	. . 3 |- F/_ x A
3	2, 2	nfpr 3639	. 2 |- F/_ x { A , A }
4	1, 3	nfcxfr 2314	1 |- F/_ x { A }

Syntax hints:   F/_wnfc 2304   {csn 3589   {cpr 3590

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-nfc 2306  df-v 2737  df-un 3131  df-sn 3595  df-pr 3596

This theorem is referenced by:  nfop  3790  nfsuc  4402  sniota  5199  dfmpo  6214