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Theorem uniun 3910
 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 1605 . . . 4
2 elun 3220 . . . . . . 7
32anbi2i 675 . . . . . 6
4 andi 837 . . . . . 6
53, 4bitri 240 . . . . 5
65exbii 1582 . . . 4
7 eluni 3894 . . . . 5
8 eluni 3894 . . . . 5
97, 8orbi12i 507 . . . 4
101, 6, 93bitr4i 268 . . 3
11 eluni 3894 . . 3
12 elun 3220 . . 3
1310, 11, 123bitr4i 268 . 2
1413eqriv 2350 1
 Colors of variables: wff setvar class Syntax hints:   wo 357   wa 358  wex 1541   wceq 1642   wcel 1710   cun 3207  cuni 3891 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-uni 3892 This theorem is referenced by:  pw1equn  4331  pw1eqadj  4332  nnadjoin  4520  fvun  5378
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