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Theorem bj-snexg 12921
Description: snexg 4076 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 3509 . 2 {𝐴} = {𝐴, 𝐴}
2 bj-prexg 12920 . . 3 ((𝐴𝑉𝐴𝑉) → {𝐴, 𝐴} ∈ V)
32anidms 392 . 2 (𝐴𝑉 → {𝐴, 𝐴} ∈ V)
41, 3eqeltrid 2202 1 (𝐴𝑉 → {𝐴} ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1463  Vcvv 2658  {csn 3495  {cpr 3496
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-14 1475  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-pr 4099  ax-bdor 12825  ax-bdeq 12829  ax-bdsep 12893
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502
This theorem is referenced by:  bj-snex  12922  bj-sels  12923  bj-sucexg  12931
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