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

Theorem ssintub 3633
 Description: Subclass of the least upper bound. (Contributed by NM, 8-Aug-2000.)
Assertion
Ref Expression
ssintub
Distinct variable groups:   ,   ,

Proof of Theorem ssintub
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssint 3631 . 2
2 sseq2 2967 . . . 4
32elrab 2698 . . 3
43simprbi 260 . 2
51, 4mprgbir 2379 1
 Colors of variables: wff set class Syntax hints:   wcel 1393  crab 2310   wss 2917  cint 3615 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-ral 2311  df-rab 2315  df-v 2559  df-in 2924  df-ss 2931  df-int 3616 This theorem is referenced by:  intmin  3635
 Copyright terms: Public domain W3C validator