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Theorem nfsn 3590
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 3545 . 2  |-  { A }  =  { A ,  A }
2 nfsn.1 . . 3  |-  F/_ x A
32, 2nfpr 3580 . 2  |-  F/_ x { A ,  A }
41, 3nfcxfr 2279 1  |-  F/_ x { A }
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2269   {csn 3531   {cpr 3532
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3079  df-sn 3537  df-pr 3538
This theorem is referenced by:  nfop  3728  nfsuc  4337  sniota  5122  dfmpo  6127
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