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Theorem bj-snex 15405
Description: snex 4214 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 15404 . 2 (𝐴 ∈ V → {𝐴} ∈ V)
31, 2ax-mp 5 1 {𝐴} ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 2164  Vcvv 2760  {csn 3618
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2167  ax-ext 2175  ax-pr 4238  ax-bdor 15308  ax-bdeq 15312  ax-bdsep 15376
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157  df-sn 3624  df-pr 3625
This theorem is referenced by:  bj-d0clsepcl  15417
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