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

Theorem intminss 3832
 Description: Under subset ordering, the intersection of a restricted class abstraction is less than or equal to any of its members. (Contributed by NM, 7-Sep-2013.)
Hypothesis
Ref Expression
intminss.1
Assertion
Ref Expression
intminss
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem intminss
StepHypRef Expression
1 intminss.1 . . 3
21elrab 2868 . 2
3 intss1 3822 . 2
42, 3sylbir 134 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1335   wcel 2128  crab 2439   wss 3102  cint 3807 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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rab 2444  df-v 2714  df-in 3108  df-ss 3115  df-int 3808 This theorem is referenced by:  onintss  4349  cardonle  7105
 Copyright terms: Public domain W3C validator