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Theorem bj-snexg 10846
Description: snexg 3958 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 3414 . 2  |-  { A }  =  { A ,  A }
2 bj-prexg 10845 . . 3  |-  ( ( A  e.  V  /\  A  e.  V )  ->  { A ,  A }  e.  _V )
32anidms 389 . 2  |-  ( A  e.  V  ->  { A ,  A }  e.  _V )
41, 3syl5eqel 2166 1  |-  ( A  e.  V  ->  { A }  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   _Vcvv 2602   {csn 3400   {cpr 3401
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-pr 3966  ax-bdor 10750  ax-bdeq 10754  ax-bdsep 10818
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-sn 3406  df-pr 3407
This theorem is referenced by:  bj-snex  10847  bj-sels  10848  bj-sucexg  10856
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