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Theorem bj-sucex 15339
Description: sucex 4523 from bounded separation. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-sucex.1 𝐴 ∈ V
Assertion
Ref Expression
bj-sucex suc 𝐴 ∈ V

Proof of Theorem bj-sucex
StepHypRef Expression
1 bj-sucex.1 . 2 𝐴 ∈ V
2 bj-sucexg 15338 . 2 (𝐴 ∈ V → suc 𝐴 ∈ V)
31, 2ax-mp 5 1 suc 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 2160  Vcvv 2756  suc csuc 4390
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-13 2162  ax-14 2163  ax-ext 2171  ax-pr 4234  ax-un 4458  ax-bd0 15229  ax-bdor 15232  ax-bdex 15235  ax-bdeq 15236  ax-bdel 15237  ax-bdsb 15238  ax-bdsep 15300
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-v 2758  df-un 3153  df-sn 3620  df-pr 3621  df-uni 3832  df-suc 4396  df-bdc 15257
This theorem is referenced by:  bj-indint  15347  bj-bdfindis  15363  bj-inf2vnlem1  15386
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