Theorem nfsn 4652

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 4581	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
2		nfsn.1	. . 3 ⊢ Ⅎ𝑥𝐴
3	2, 2	nfpr 4637	. 2 ⊢ Ⅎ𝑥{𝐴, 𝐴}
4	1, 3	nfcxfr 2897	1 ⊢ Ⅎ𝑥{𝐴}

Syntax hints:  Ⅎwnfc 2884  {csn 4568  {cpr 4570

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-10 2147  ax-11 2163  ax-12 2185  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-nf 1786  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-nfc 2886  df-v 3432  df-un 3895  df-sn 4569  df-pr 4571

This theorem is referenced by:  nfop  4833  iunopeqop  5469  nfpred  6264  nfsuc  6391  sniota  6483  dfmpo  8045  nosupbnd2  27694  noinfbnd2  27709  bnj958  35098  bnj1000  35099  bnj1446  35203  bnj1447  35204  bnj1448  35205  bnj1466  35211  bnj1467  35212  nfaltop  36178  stoweidlem21  46467  stoweidlem47  46493  nfdfat  47587