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Theorem bj-snex 11804
Description: snex 4020 from bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-snex.1 𝐴 ∈ V
Assertion
Ref Expression
bj-snex {𝐴} ∈ V

Proof of Theorem bj-snex
StepHypRef Expression
1 bj-snex.1 . 2 𝐴 ∈ V
2 bj-snexg 11803 . 2 (𝐴 ∈ V → {𝐴} ∈ V)
31, 2ax-mp 7 1 {𝐴} ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1438  Vcvv 2619  {csn 3446
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 4036  ax-bdor 11707  ax-bdeq 11711  ax-bdsep 11775
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 3452  df-pr 3453
This theorem is referenced by:  bj-d0clsepcl  11820
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