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Theorem bj-uniex 7287
Description: uniex 4124 from bounded separation. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-uniex.1 A V
Assertion
Ref Expression
bj-uniex A V

Proof of Theorem bj-uniex
Dummy variables x y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bj-uniex.1 . 2 A V
2 unieq 3563 . . 3 (x = A x = A)
32eleq1d 2088 . 2 (x = A → ( x V ↔ A V))
4 bj-uniex2 7286 . . 3 y y = x
54issetri 2542 . 2 x V
61, 3, 5vtocl 2585 1 A V
Colors of variables: wff set class
Syntax hints:   = wceq 1228   wcel 1374  Vcvv 2535   cuni 3554
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-13 1385  ax-14 1386  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-un 4120  ax-bd0 7187  ax-bdex 7193  ax-bdel 7195  ax-bdsb 7196  ax-bdsep 7258
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290  df-v 2537  df-uni 3555  df-bdc 7215
This theorem is referenced by:  bj-uniexg  7288  bj-unex  7289
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