Theorem nfsn 4654

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 4585	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
2		nfsn.1	. . 3 ⊢ Ⅎ𝑥𝐴
3	2, 2	nfpr 4637	. 2 ⊢ Ⅎ𝑥{𝐴, 𝐴}
4	1, 3	nfcxfr 2902	1 ⊢ Ⅎ𝑥{𝐴}

Syntax hints:  Ⅎwnfc 2884  {csn 4572  {cpr 4574

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2153  ax-12 2170  ax-ext 2707

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1543  df-ex 1781  df-nf 1785  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-nfc 2886  df-v 3443  df-un 3902  df-sn 4573  df-pr 4575

This theorem is referenced by:  nfop  4832  iunopeqop  5459  nfpred  6237  nfsuc  6367  sniota  6464  dfmpo  8002  nosupbnd2  26962  noinfbnd2  26977  bnj958  33132  bnj1000  33133  bnj1446  33237  bnj1447  33238  bnj1448  33239  bnj1466  33245  bnj1467  33246  nfaltop  34373  stoweidlem21  43887  stoweidlem47  43913  nfdfat  44959