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Theorem nfsn 3704
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 3667 . 2  |-  { A }  =  { A ,  A }
2 nfsn.1 . . 3  |-  F/_ x A
32, 2nfpr 3693 . 2  |-  F/_ x { A ,  A }
41, 3nfcxfr 2429 1  |-  F/_ x { A }
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2419   {csn 3653   {cpr 3654
This theorem is referenced by:  nfop  3828  nfsuc  4479  sniota  5262  dfmpt2  6225  nfaltop  24586  stoweidlem21  27873  stoweidlem47  27899  nfdfat  28098  bnj958  29288  bnj1000  29289  bnj1446  29391  bnj1447  29392  bnj1448  29393  bnj1466  29399  bnj1467  29400
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-sn 3659  df-pr 3660
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