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Theorem bj-uniex 10037
 Description: uniex 4174 from bounded separation. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-uniex.1
Assertion
Ref Expression
bj-uniex

Proof of Theorem bj-uniex
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bj-uniex.1 . 2
2 unieq 3589 . . 3
32eleq1d 2106 . 2
4 bj-uniex2 10036 . . 3
54issetri 2564 . 2
61, 3, 5vtocl 2608 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   wcel 1393  cvv 2557  cuni 3580 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-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-un 4170  ax-bd0 9933  ax-bdex 9939  ax-bdel 9941  ax-bdsb 9942  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-rex 2312  df-v 2559  df-uni 3581  df-bdc 9961 This theorem is referenced by:  bj-uniexg  10038  bj-unex  10039
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