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Theorem uniun 3640
 Description: The class union of the union of two classes. Theorem 8.3 of [Quine] p. 53. (Contributed by NM, 20-Aug-1993.)
Assertion
Ref Expression
uniun

Proof of Theorem uniun
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 19.43 1560 . . . 4
2 elun 3123 . . . . . . 7
32anbi2i 445 . . . . . 6
4 andi 765 . . . . . 6
53, 4bitri 182 . . . . 5
65exbii 1537 . . . 4
7 eluni 3624 . . . . 5
8 eluni 3624 . . . . 5
97, 8orbi12i 714 . . . 4
101, 6, 93bitr4i 210 . . 3
11 eluni 3624 . . 3
12 elun 3123 . . 3
1310, 11, 123bitr4i 210 . 2
1413eqriv 2080 1
 Colors of variables: wff set class Syntax hints:   wa 102   wo 662   wceq 1285  wex 1422   wcel 1434   cun 2980  cuni 3621 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986  df-uni 3622 This theorem is referenced by:  unisuc  4196  unisucg  4197
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