Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  iuncom4 Unicode version

Theorem iuncom4 3692
 Description: Commutation of union with indexed union. (Contributed by Mario Carneiro, 18-Jan-2014.)
Assertion
Ref Expression
iuncom4

Proof of Theorem iuncom4
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-rex 2329 . . . . . . 7
21rexbii 2348 . . . . . 6
3 rexcom4 2594 . . . . . 6
42, 3bitri 177 . . . . 5
5 r19.41v 2483 . . . . . 6
65exbii 1512 . . . . 5
74, 6bitri 177 . . . 4
8 eluni2 3612 . . . . 5
98rexbii 2348 . . . 4
10 df-rex 2329 . . . . 5
11 eliun 3689 . . . . . . 7
1211anbi1i 439 . . . . . 6
1312exbii 1512 . . . . 5
1410, 13bitri 177 . . . 4
157, 9, 143bitr4i 205 . . 3
16 eliun 3689 . . 3
17 eluni2 3612 . . 3
1815, 16, 173bitr4i 205 . 2
1918eqriv 2053 1
 Colors of variables: wff set class Syntax hints:   wa 101   wceq 1259  wex 1397   wcel 1409  wrex 2324  cuni 3608  ciun 3685 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-uni 3609  df-iun 3687 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator