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Theorem iunxun 4047
 Description: Separate a union in the index of an indexed union. (Contributed by NM, 26-Mar-2004.) (Proof shortened by Mario Carneiro, 17-Nov-2016.)
Assertion
Ref Expression
iunxun

Proof of Theorem iunxun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 rexun 3443 . . . 4
2 eliun 3973 . . . . 5
3 eliun 3973 . . . . 5
42, 3orbi12i 507 . . . 4
51, 4bitr4i 243 . . 3
6 eliun 3973 . . 3
7 elun 3220 . . 3
85, 6, 73bitr4i 268 . 2
98eqriv 2350 1
 Colors of variables: wff setvar class Syntax hints:   wo 357   wceq 1642   wcel 1710  wrex 2615   cun 3207  ciun 3969 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-iun 3971 This theorem is referenced by: (None)
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