Theorem nfsn 3785

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

Hypothesis

Ref	Expression
nfsn.1	|- F/_xA

Assertion

Ref	Expression
nfsn	|- F/_x{A}

Proof of Theorem nfsn

Step	Hyp	Ref	Expression
1		dfsn2 3748	. 2 |- {A} = {A, A}
2		nfsn.1	. . 3 |- F/_xA
3	2, 2	nfpr 3774	. 2 |- F/_x{A, A}
4	1, 3	nfcxfr 2487	1 |- F/_x{A}

Syntax hints:   F/_wnfc 2477  {csn 3738  {cpr 3739

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-v 2862  df-nin 3212  df-compl 3213  df-un 3215  df-sn 3742  df-pr 3743

This theorem is referenced by:  nfopk  4069  sniota  4370