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Theorem bj-snexg 10005
Description: snexg 3936 from bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-snexg  |-  ( A  e.  V  ->  { A }  e.  _V )

Proof of Theorem bj-snexg
StepHypRef Expression
1 dfsn2 3389 . 2  |-  { A }  =  { A ,  A }
2 bj-prexg 10004 . . 3  |-  ( ( A  e.  V  /\  A  e.  V )  ->  { A ,  A }  e.  _V )
32anidms 377 . 2  |-  ( A  e.  V  ->  { A ,  A }  e.  _V )
41, 3syl5eqel 2124 1  |-  ( A  e.  V  ->  { A }  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1393   _Vcvv 2557   {csn 3375   {cpr 3376
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-pr 3944  ax-bdor 9909  ax-bdeq 9913  ax-bdsep 9977
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382
This theorem is referenced by:  bj-snex  10006  bj-sels  10007  bj-sucexg  10015
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