Theorem nfsn 4242

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 4190	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
2		nfsn.1	. . 3 ⊢ Ⅎ𝑥𝐴
3	2, 2	nfpr 4232	. 2 ⊢ Ⅎ𝑥{𝐴, 𝐴}
4	1, 3	nfcxfr 2762	1 ⊢ Ⅎ𝑥{𝐴}

Syntax hints:  Ⅎwnfc 2751  {csn 4177  {cpr 4179

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-sn 4178  df-pr 4180

This theorem is referenced by:  nfop  4418  iunopeqop  4981  nfpred  5685  nfsuc  5796  sniota  5878  dfmpt2  7267  bnj958  31010  bnj1000  31011  bnj1446  31113  bnj1447  31114  bnj1448  31115  bnj1466  31121  bnj1467  31122  nosupbnd2  31862  nfaltop  32087  stoweidlem21  40238  stoweidlem47  40264  nfdfat  41210