Theorem intminss 4313

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:   ,   ,   ,

Proof of Theorem intminss

Step	Hyp	Ref	Expression
1		intminss.1	. . 3
2	1	elrab 3257	. 2
3		intss1 4301	. 2
4	2, 3	sylbir 213	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  {crab 2811  C_wss 3475  |^|cint 4286

This theorem is referenced by:  onintss  4933  knatar  6253  cardonle  8359  coftr  8674  wuncss  9144  ist1-3  19850  sigagenss  28149  nodenselem5  29445  nobndlem6  29457  nobndlem8  29459  fneint  30166  igenmin  30461  pclclN  35615

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-in 3482  df-ss 3489  df-int 4287