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Theorem bj-snexg 10861
Description: snexg 3964 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 3420 . 2 {𝐴} = {𝐴, 𝐴}
2 bj-prexg 10860 . . 3 ((𝐴𝑉𝐴𝑉) → {𝐴, 𝐴} ∈ V)
32anidms 389 . 2 (𝐴𝑉 → {𝐴, 𝐴} ∈ V)
41, 3syl5eqel 2166 1 (𝐴𝑉 → {𝐴} ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1434  Vcvv 2602  {csn 3406  {cpr 3407
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 3972  ax-bdor 10765  ax-bdeq 10769  ax-bdsep 10833
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 3412  df-pr 3413
This theorem is referenced by:  bj-snex  10862  bj-sels  10863  bj-sucexg  10871
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