ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ssun3 GIF version

Theorem ssun3 3133
Description: Subclass law for union of classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
ssun3 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))

Proof of Theorem ssun3
StepHypRef Expression
1 ssun1 3131 . 2 𝐵 ⊆ (𝐵𝐶)
2 sstr2 2977 . 2 (𝐴𝐵 → (𝐵 ⊆ (𝐵𝐶) → 𝐴 ⊆ (𝐵𝐶)))
31, 2mpi 15 1 (𝐴𝐵𝐴 ⊆ (𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  cun 2940  wss 2942
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 638  ax-5 1350  ax-7 1351  ax-gen 1352  ax-ie1 1396  ax-ie2 1397  ax-8 1409  ax-10 1410  ax-11 1411  ax-i12 1412  ax-bndl 1413  ax-4 1414  ax-17 1433  ax-i9 1437  ax-ial 1441  ax-i5r 1442  ax-ext 2036
This theorem depends on definitions:  df-bi 114  df-tru 1260  df-nf 1364  df-sb 1660  df-clab 2041  df-cleq 2047  df-clel 2050  df-nfc 2181  df-v 2574  df-un 2947  df-in 2949  df-ss 2956
This theorem is referenced by:  ssun  3147  xpsspw  4475
  Copyright terms: Public domain W3C validator