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

Theorem unundi 3104
 Description: Union distributes over itself. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
unundi (𝐴 ∪ (𝐵𝐶)) = ((𝐴𝐵) ∪ (𝐴𝐶))

Proof of Theorem unundi
StepHypRef Expression
1 unidm 3086 . . 3 (𝐴𝐴) = 𝐴
21uneq1i 3093 . 2 ((𝐴𝐴) ∪ (𝐵𝐶)) = (𝐴 ∪ (𝐵𝐶))
3 un4 3103 . 2 ((𝐴𝐴) ∪ (𝐵𝐶)) = ((𝐴𝐵) ∪ (𝐴𝐶))
42, 3eqtr3i 2062 1 (𝐴 ∪ (𝐵𝐶)) = ((𝐴𝐵) ∪ (𝐴𝐶))
 Colors of variables: wff set class Syntax hints:   = wceq 1243   ∪ cun 2915 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-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-un 2922 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator