Theorem nfsn 4636

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 4573	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
2		nfsn.1	. . 3 ⊢ Ⅎ𝑥𝐴
3	2, 2	nfpr 4621	. 2 ⊢ Ⅎ𝑥{𝐴, 𝐴}
4	1, 3	nfcxfr 2975	1 ⊢ Ⅎ𝑥{𝐴}

Syntax hints:  Ⅎwnfc 2961  {csn 4560  {cpr 4562

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-v 3496  df-un 3940  df-sn 4561  df-pr 4563

This theorem is referenced by:  nfop  4812  iunopeqop  5403  nfpred  6147  nfsuc  6256  sniota  6340  dfmpo  7791  bnj958  32207  bnj1000  32208  bnj1446  32312  bnj1447  32313  bnj1448  32314  bnj1466  32320  bnj1467  32321  nosupbnd2  33211  nfaltop  33436  stoweidlem21  42300  stoweidlem47  42326  nfdfat  43320