Theorem nfsn 4666

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 4595	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
2		nfsn.1	. . 3 ⊢ Ⅎ𝑥𝐴
3	2, 2	nfpr 4651	. 2 ⊢ Ⅎ𝑥{𝐴, 𝐴}
4	1, 3	nfcxfr 2897	1 ⊢ Ⅎ𝑥{𝐴}

Syntax hints:  Ⅎwnfc 2884  {csn 4582  {cpr 4584

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-10 2147  ax-11 2163  ax-12 2185  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-nf 1786  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-nfc 2886  df-v 3444  df-un 3908  df-sn 4583  df-pr 4585

This theorem is referenced by:  nfop  4847  iunopeqop  5477  nfpred  6272  nfsuc  6399  sniota  6491  dfmpo  8054  nosupbnd2  27696  noinfbnd2  27711  bnj958  35116  bnj1000  35117  bnj1446  35221  bnj1447  35222  bnj1448  35223  bnj1466  35229  bnj1467  35230  nfaltop  36196  stoweidlem21  46379  stoweidlem47  46405  nfdfat  47487