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

Theorem iinuni 4049
 Description: A relationship involving union and indexed intersection. Exercise 23 of [Enderton] p. 33. (Contributed by NM, 25-Nov-2003.) (Proof shortened by Mario Carneiro, 17-Nov-2016.)
Assertion
Ref Expression
iinuni
Distinct variable groups:   ,   ,

Proof of Theorem iinuni
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 r19.32v 2757 . . . 4
2 elun 3220 . . . . 5
32ralbii 2638 . . . 4
4 vex 2862 . . . . . 6
54elint2 3933 . . . . 5
65orbi2i 505 . . . 4
71, 3, 63bitr4ri 269 . . 3
8 elun 3220 . . 3
9 eliin 3974 . . . 4
104, 9ax-mp 8 . . 3
117, 8, 103bitr4i 268 . 2
1211eqriv 2350 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wo 357   wceq 1642   wcel 1710  wral 2614  cvv 2859   cun 3207  cint 3926  ciin 3970 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-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-int 3927  df-iin 3972 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator