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Theorem snex 3928
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 3927 . 2 (A V → {A} V)
31, 2ax-mp 7 1 {A} V
Colors of variables: wff set class
Syntax hints:   wcel 1390  Vcvv 2551  {csn 3367
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373
This theorem is referenced by:  ensn1  6212  xpsnen  6231  endisj  6234  xpcomco  6236  xpassen  6240  nn0ex  7923
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