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

Theorem ssun2 3235
Description: Subclass relationship for union of classes. (Contributed by NM, 30-Aug-1993.)
Assertion
Ref Expression
ssun2  |-  A  C_  ( B  u.  A
)

Proof of Theorem ssun2
StepHypRef Expression
1 ssun1 3234 . 2  |-  A  C_  ( A  u.  B
)
2 uncom 3215 . 2  |-  ( A  u.  B )  =  ( B  u.  A
)
31, 2sseqtri 3126 1  |-  A  C_  ( B  u.  A
)
Colors of variables: wff set class
Syntax hints:    u. cun 3064    C_ wss 3066
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-ss 3079
This theorem is referenced by:  ssun4  3237  elun2  3239  unv  3395  un00  3404  snsspr2  3664  snsstp3  3667  unexb  4358  rnexg  4799  brtpos0  6142  ac6sfi  6785  caserel  6965  pnfxr  7811  ltrelxr  7818  un0mulcl  9004  fsumsplit  11169  bdunexb  13107
  Copyright terms: Public domain W3C validator