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Theorem uniun 3750
 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 1607 . . . 4
2 elun 3212 . . . . . . 7
32anbi2i 452 . . . . . 6
4 andi 807 . . . . . 6
53, 4bitri 183 . . . . 5
65exbii 1584 . . . 4
7 eluni 3734 . . . . 5
8 eluni 3734 . . . . 5
97, 8orbi12i 753 . . . 4
101, 6, 93bitr4i 211 . . 3
11 eluni 3734 . . 3
12 elun 3212 . . 3
1310, 11, 123bitr4i 211 . 2
1413eqriv 2134 1
 Colors of variables: wff set class Syntax hints:   wa 103   wo 697   wceq 1331  wex 1468   wcel 1480   cun 3064  cuni 3731 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-uni 3732 This theorem is referenced by:  unisuc  4330  unisucg  4331
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