Theorem nfsn 4189

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 4138	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
2		nfsn.1	. . 3 ⊢ Ⅎ𝑥𝐴
3	2, 2	nfpr 4179	. 2 ⊢ Ⅎ𝑥{𝐴, 𝐴}
4	1, 3	nfcxfr 2749	1 ⊢ Ⅎ𝑥{𝐴}

Syntax hints:  Ⅎwnfc 2738  {csn 4125  {cpr 4127

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-sn 4126  df-pr 4128

This theorem is referenced by:  nfop  4356  iunopeqop  4906  nfpred  5602  nfsuc  5713  sniota  5795  dfmpt2  7154  bnj958  30264  bnj1000  30265  bnj1446  30367  bnj1447  30368  bnj1448  30369  bnj1466  30375  bnj1467  30376  nfaltop  31257  stoweidlem21  38914  stoweidlem47  38940  nfdfat  39859