New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  iunun Unicode version

Theorem iunun 4046
 Description: Separate a union in an indexed union. (Contributed by NM, 27-Dec-2004.) (Proof shortened by Mario Carneiro, 17-Nov-2016.)
Assertion
Ref Expression
iunun

Proof of Theorem iunun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 r19.43 2766 . . . 4
2 elun 3220 . . . . 5
32rexbii 2639 . . . 4
4 eliun 3973 . . . . 5
5 eliun 3973 . . . . 5
64, 5orbi12i 507 . . . 4
71, 3, 63bitr4i 268 . . 3
8 eliun 3973 . . 3
9 elun 3220 . . 3
107, 8, 93bitr4i 268 . 2
1110eqriv 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:  iununi  4050
 Copyright terms: Public domain W3C validator