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Theorem snex 3965
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  e. 
_V
Assertion
Ref Expression
snex  |-  { A }  e.  _V

Proof of Theorem snex
StepHypRef Expression
1 snex.1 . 2  |-  A  e. 
_V
2 snexg 3964 . 2  |-  ( A  e.  _V  ->  { A }  e.  _V )
31, 2ax-mp 7 1  |-  { A }  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1409   _Vcvv 2574   {csn 3403
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pow 3955
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-in 2952  df-ss 2959  df-pw 3389  df-sn 3409
This theorem is referenced by:  ensn1  6307  xpsnen  6326  endisj  6329  xpcomco  6331  xpassen  6335  phplem2  6347  findcard2  6377  findcard2s  6378  ac6sfi  6383  nn0ex  8245
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