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Theorem bj-snex 10033
 Description: snex 3937 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 10032 . 2 (𝐴 ∈ V → {𝐴} ∈ V)
31, 2ax-mp 7 1 {𝐴} ∈ V
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1393  Vcvv 2557  {csn 3375 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-pr 3944  ax-bdor 9936  ax-bdeq 9940  ax-bdsep 10004 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382 This theorem is referenced by:  bj-d0clsepcl  10049
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