Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  dmiun Unicode version

Theorem dmiun 4748
 Description: The domain of an indexed union. (Contributed by Mario Carneiro, 26-Apr-2016.)
Assertion
Ref Expression
dmiun

Proof of Theorem dmiun
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rexcom4 2709 . . . 4
2 vex 2689 . . . . . 6
32eldm2 4737 . . . . 5
43rexbii 2442 . . . 4
5 eliun 3817 . . . . 5
65exbii 1584 . . . 4
71, 4, 63bitr4ri 212 . . 3
82eldm2 4737 . . 3
9 eliun 3817 . . 3
107, 8, 93bitr4i 211 . 2
1110eqriv 2136 1
 Colors of variables: wff set class Syntax hints:   wceq 1331  wex 1468   wcel 1480  wrex 2417  cop 3530  ciun 3813   cdm 4539 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-iun 3815  df-br 3930  df-dm 4549 This theorem is referenced by:  ennnfonelemdm  11944
 Copyright terms: Public domain W3C validator