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Theorem bj-snexg 13869
Description: snexg 4168 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 3595 . 2  |-  { A }  =  { A ,  A }
2 bj-prexg 13868 . . 3  |-  ( ( A  e.  V  /\  A  e.  V )  ->  { A ,  A }  e.  _V )
32anidms 395 . 2  |-  ( A  e.  V  ->  { A ,  A }  e.  _V )
41, 3eqeltrid 2257 1  |-  ( A  e.  V  ->  { A }  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2141   _Vcvv 2730   {csn 3581   {cpr 3582
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-14 2144  ax-ext 2152  ax-pr 4192  ax-bdor 13773  ax-bdeq 13777  ax-bdsep 13841
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-sn 3587  df-pr 3588
This theorem is referenced by:  bj-snex  13870  bj-sels  13871  bj-sucexg  13879
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