Theorem nfsn 4674

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 4605	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
2		nfsn.1	. . 3 ⊢ Ⅎ𝑥𝐴
3	2, 2	nfpr 4659	. 2 ⊢ Ⅎ𝑥{𝐴, 𝐴}
4	1, 3	nfcxfr 2890	1 ⊢ Ⅎ𝑥{𝐴}

Syntax hints:  Ⅎwnfc 2877  {csn 4592  {cpr 4594

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 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2702

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 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-nfc 2879  df-v 3452  df-un 3922  df-sn 4593  df-pr 4595

This theorem is referenced by:  nfop  4856  iunopeqop  5484  nfpred  6282  nfsuc  6409  sniota  6505  dfmpo  8084  nosupbnd2  27635  noinfbnd2  27650  bnj958  34937  bnj1000  34938  bnj1446  35042  bnj1447  35043  bnj1448  35044  bnj1466  35050  bnj1467  35051  nfaltop  35975  stoweidlem21  46026  stoweidlem47  46052  nfdfat  47132