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Theorem snex 3889
Description: A singleton whose element exists is a set. (Contributed by NM, 7-Aug-1994.) (Revised by Mario Carneiro, 24-May-2019.)
Hypothesis
Ref Expression
snex.1 A V
Assertion
Ref Expression
snex {A} V

Proof of Theorem snex
StepHypRef Expression
1 snex.1 . 2 A V
2 snexg 3888 . 2 (A V → {A} V)
31, 2ax-mp 7 1 {A} V
Colors of variables: wff set class
Syntax hints:   wcel 1375  Vcvv 2533  {csn 3327
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1315  ax-7 1316  ax-gen 1317  ax-ie1 1362  ax-ie2 1363  ax-8 1377  ax-10 1378  ax-11 1379  ax-i12 1380  ax-bnd 1381  ax-4 1382  ax-14 1387  ax-17 1401  ax-i9 1405  ax-ial 1410  ax-i5r 1411  ax-ext 2004  ax-sep 3827  ax-pow 3879
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1329  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2535  df-in 2902  df-ss 2909  df-pw 3313  df-sn 3333
This theorem is referenced by: (None)
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