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Theorem nfsn 3430
 Description: Bound-variable hypothesis builder for singletons. (Contributed by NM, 14-Nov-1995.)
Hypothesis
Ref Expression
nfsn.1 𝑥𝐴
Assertion
Ref Expression
nfsn 𝑥{𝐴}

Proof of Theorem nfsn
StepHypRef Expression
1 dfsn2 3389 . 2 {𝐴} = {𝐴, 𝐴}
2 nfsn.1 . . 3 𝑥𝐴
32, 2nfpr 3420 . 2 𝑥{𝐴, 𝐴}
41, 3nfcxfr 2175 1 𝑥{𝐴}
 Colors of variables: wff set class Syntax hints:  Ⅎwnfc 2165  {csn 3375  {cpr 3376 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382 This theorem is referenced by:  nfop  3565  nfsuc  4145  sniota  4894  dfmpt2  5844
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