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Theorem intminss 4076
 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 3092 . 2
3 intss1 4065 . 2
42, 3sylbir 205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  crab 2709   wss 3320  cint 4050 This theorem is referenced by:  onintss  4631  knatar  6080  cardonle  7844  coftr  8153  wuncss  8620  ist1-3  17413  sigagenss  24532  nodenselem5  25640  nobndlem6  25652  nobndlem8  25654  fneint  26357  igenmin  26674  pclclN  30688 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-in 3327  df-ss 3334  df-int 4051
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