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Theorem nfsn 3476
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 3436 . 2  |-  { A }  =  { A ,  A }
2 nfsn.1 . . 3  |-  F/_ x A
32, 2nfpr 3466 . 2  |-  F/_ x { A ,  A }
41, 3nfcxfr 2220 1  |-  F/_ x { A }
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2210   {csn 3422   {cpr 3423
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614  df-un 2988  df-sn 3428  df-pr 3429
This theorem is referenced by:  nfop  3612  nfsuc  4198  sniota  4959  dfmpt2  5921
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