Theorem nfsn 4683

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

Hypothesis

Ref	Expression
nfsn.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfsn	⊢ Ⅎ𝑥{𝐴}

Proof of Theorem nfsn

Step	Hyp	Ref	Expression
1		dfsn2 4614	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
2		nfsn.1	. . 3 ⊢ Ⅎ𝑥𝐴
3	2, 2	nfpr 4668	. 2 ⊢ Ⅎ𝑥{𝐴, 𝐴}
4	1, 3	nfcxfr 2896	1 ⊢ Ⅎ𝑥{𝐴}

Syntax hints:  Ⅎwnfc 2883  {csn 4601  {cpr 4603

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-nfc 2885  df-v 3461  df-un 3931  df-sn 4602  df-pr 4604

This theorem is referenced by:  nfop  4865  iunopeqop  5496  nfpred  6295  nfsuc  6426  sniota  6522  dfmpo  8101  nosupbnd2  27680  noinfbnd2  27695  bnj958  34971  bnj1000  34972  bnj1446  35076  bnj1447  35077  bnj1448  35078  bnj1466  35084  bnj1467  35085  nfaltop  35998  stoweidlem21  46050  stoweidlem47  46076  nfdfat  47156