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Theorem uniun 4026
 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 1615 . . . 4
2 elun 3480 . . . . . . 7
32anbi2i 676 . . . . . 6
4 andi 838 . . . . . 6
53, 4bitri 241 . . . . 5
65exbii 1592 . . . 4
7 eluni 4010 . . . . 5
8 eluni 4010 . . . . 5
97, 8orbi12i 508 . . . 4
101, 6, 93bitr4i 269 . . 3
11 eluni 4010 . . 3
12 elun 3480 . . 3
1310, 11, 123bitr4i 269 . 2
1413eqriv 2432 1
 Colors of variables: wff set class Syntax hints:   wo 358   wa 359  wex 1550   wceq 1652   wcel 1725   cun 3310  cuni 4007 This theorem is referenced by:  unidif0  4364  unisuc  4649  onuninsuci  4811  fvssunirn  5745  fvun  5784  tc2  7670  fin1a2lem10  8278  fin1a2lem12  8280  incexclem  12604  dprd2da  15588  dmdprdsplit2lem  15591  ordtuni  17242  cmpcld  17453  uncmp  17454  1stckgenlem  17573  filcon  17903  ufildr  17951  alexsubALTlem3  18068  cldsubg  18128  icccmplem2  18842  uniioombllem3  19465  sxbrsigalem0  24609  cvmscld  24948  mbfresfi  26199  refssfne  26311  topjoin  26331 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-uni 4008
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