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Theorem nfsn 3866
Description: Bound-variable hypothesis builder for singletons. (Contributed by NM, 14-Nov-1995.)
Hypothesis
Ref Expression
nfsn.1  |-  F/_ x A
Assertion
Ref Expression
nfsn  |-  F/_ x { A }

Proof of Theorem nfsn
StepHypRef Expression
1 dfsn2 3828 . 2  |-  { A }  =  { A ,  A }
2 nfsn.1 . . 3  |-  F/_ x A
32, 2nfpr 3855 . 2  |-  F/_ x { A ,  A }
41, 3nfcxfr 2569 1  |-  F/_ x { A }
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2559   {csn 3814   {cpr 3815
This theorem is referenced by:  nfop  4000  nfsuc  4652  sniota  5445  dfmpt2  6437  nfpred  25444  nfaltop  25825  stoweidlem21  27746  stoweidlem47  27772  nfdfat  27970  bnj958  29311  bnj1000  29312  bnj1446  29414  bnj1447  29415  bnj1448  29416  bnj1466  29422  bnj1467  29423
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-un 3325  df-sn 3820  df-pr 3821
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