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Theorem nfsn 3664
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 3618 . 2 {𝐴} = {𝐴, 𝐴}
2 nfsn.1 . . 3 𝑥𝐴
32, 2nfpr 3654 . 2 𝑥{𝐴, 𝐴}
41, 3nfcxfr 2326 1 𝑥{𝐴}
Colors of variables: wff set class
Syntax hints:  wnfc 2316  {csn 3604  {cpr 3605
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-un 3145  df-sn 3610  df-pr 3611
This theorem is referenced by:  nfop  3806  nfsuc  4420  sniota  5219  dfmpo  6238
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