Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  unidif0 Unicode version

Theorem unidif0 3920
 Description: The removal of the empty set from a class does not affect its union. (Contributed by NM, 22-Mar-2004.)
Assertion
Ref Expression
unidif0

Proof of Theorem unidif0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 n0i 3229 . . . . . . 7
21pm4.71i 371 . . . . . 6
32anbi1i 431 . . . . 5
4 an32 496 . . . . 5
5 anass 381 . . . . 5
63, 4, 53bitr2ri 198 . . . 4
76exbii 1496 . . 3
8 eluni 3583 . . . 4
9 eldif 2927 . . . . . . 7
10 velsn 3392 . . . . . . . . 9
1110notbii 594 . . . . . . . 8
1211anbi2i 430 . . . . . . 7
139, 12bitri 173 . . . . . 6
1413anbi2i 430 . . . . 5
1514exbii 1496 . . . 4
168, 15bitri 173 . . 3
17 eluni 3583 . . 3
187, 16, 173bitr4i 201 . 2
1918eqriv 2037 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 97   wceq 1243  wex 1381   wcel 1393   cdif 2914  c0 3224  csn 3375  cuni 3580 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-dif 2920  df-nul 3225  df-sn 3381  df-uni 3581 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator