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Theorem bj-snexg 15349
Description: snexg 4213 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 3632 . 2  |-  { A }  =  { A ,  A }
2 bj-prexg 15348 . . 3  |-  ( ( A  e.  V  /\  A  e.  V )  ->  { A ,  A }  e.  _V )
32anidms 397 . 2  |-  ( A  e.  V  ->  { A ,  A }  e.  _V )
41, 3eqeltrid 2280 1  |-  ( A  e.  V  ->  { A }  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2164   _Vcvv 2760   {csn 3618   {cpr 3619
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2167  ax-ext 2175  ax-pr 4238  ax-bdor 15253  ax-bdeq 15257  ax-bdsep 15321
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157  df-sn 3624  df-pr 3625
This theorem is referenced by:  bj-snex  15350  bj-sels  15351  bj-sucexg  15359
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