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Theorem bj-snexg 11686
Description: snexg 4017 from bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-snexg (𝐴𝑉 → {𝐴} ∈ V)

Proof of Theorem bj-snexg
StepHypRef Expression
1 dfsn2 3458 . 2 {𝐴} = {𝐴, 𝐴}
2 bj-prexg 11685 . . 3 ((𝐴𝑉𝐴𝑉) → {𝐴, 𝐴} ∈ V)
32anidms 389 . 2 (𝐴𝑉 → {𝐴, 𝐴} ∈ V)
41, 3syl5eqel 2174 1 (𝐴𝑉 → {𝐴} ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1438  Vcvv 2619  {csn 3444  {cpr 3445
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-pr 4034  ax-bdor 11590  ax-bdeq 11594  ax-bdsep 11658
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3003  df-sn 3450  df-pr 3451
This theorem is referenced by:  bj-snex  11687  bj-sels  11688  bj-sucexg  11696
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