Theorem nfsn 4706

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 4636	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
2		nfsn.1	. . 3 ⊢ Ⅎ𝑥𝐴
3	2, 2	nfpr 4689	. 2 ⊢ Ⅎ𝑥{𝐴, 𝐴}
4	1, 3	nfcxfr 2890	1 ⊢ Ⅎ𝑥{𝐴}

Syntax hints:  Ⅎwnfc 2876  {csn 4623  {cpr 4625

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2167  ax-ext 2697

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1537  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-nfc 2878  df-v 3464  df-un 3951  df-sn 4624  df-pr 4626

This theorem is referenced by:  nfop  4887  iunopeqop  5519  nfpred  6309  nfsuc  6440  sniota  6537  dfmpo  8108  nosupbnd2  27743  noinfbnd2  27758  bnj958  34798  bnj1000  34799  bnj1446  34903  bnj1447  34904  bnj1448  34905  bnj1466  34911  bnj1467  34912  nfaltop  35817  stoweidlem21  45678  stoweidlem47  45704  nfdfat  46776