Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ssun2 GIF version

Theorem ssun2 3245
 Description: Subclass relationship for union of classes. (Contributed by NM, 30-Aug-1993.)
Assertion
Ref Expression
ssun2 𝐴 ⊆ (𝐵𝐴)

Proof of Theorem ssun2
StepHypRef Expression
1 ssun1 3244 . 2 𝐴 ⊆ (𝐴𝐵)
2 uncom 3225 . 2 (𝐴𝐵) = (𝐵𝐴)
31, 2sseqtri 3136 1 𝐴 ⊆ (𝐵𝐴)
 Colors of variables: wff set class Syntax hints:   ∪ cun 3074   ⊆ wss 3076 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3080  df-in 3082  df-ss 3089 This theorem is referenced by:  ssun4  3247  elun2  3249  unv  3405  un00  3414  snsspr2  3677  snsstp3  3680  unexb  4371  rnexg  4812  brtpos0  6157  ac6sfi  6800  caserel  6980  pnfxr  7843  ltrelxr  7850  un0mulcl  9036  fsumsplit  11209  bdunexb  13290
 Copyright terms: Public domain W3C validator