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Theorem sseqin2 3552
Description: A relationship between subclass and intersection. Similar to Exercise 9 of [TakeutiZaring] p. 18. (Contributed by NM, 17-May-1994.)
Assertion
Ref Expression
sseqin2  |-  ( A 
C_  B  <->  ( B  i^i  A )  =  A )

Proof of Theorem sseqin2
StepHypRef Expression
1 dfss1 3537 1  |-  ( A 
C_  B  <->  ( B  i^i  A )  =  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1652    i^i cin 3311    C_ wss 3312
This theorem is referenced by:  dfss4  3567  resabs1  5167  rescnvcnv  5324  fiint  7375  infxpenlem  7887  ackbij1lem2  8093  nn0supp  10265  uzin  10510  iooval2  10941  fzval2  11038  fz1isolem  11702  dfphi2  13155  ressbas  13511  ressress  13518  sylow3lem2  15254  gsumxp  15542  pgpfac1lem5  15629  cmpsub  17455  fbasrn  17908  cmmbl  19421  voliunlem3  19438  0plef  19556  0pledm  19557  itg1ge0  19570  mbfi1fseqlem5  19603  itg2addlem  19642  dvcmulf  19823  efopn  20541  cmcmlem  23085  pjvec  23190  pjocvec  23191  ssmd2  23807  mdslmd4i  23828  chirredlem2  23886  chirredlem3  23887  dmdbr7ati  23919  lmxrge0  24329  orvcelval  24718  dfon2lem4  25405  sspred  25439  predon  25460  wfrlem4  25533  frrlem4  25577  mblfinlem2  26235  blssp  26453  fsuppeq  27227  lcvexchlem1  29769  glbconN  30111  pmapglb2N  30505  pmapglb2xN  30506  2polssN  30649  polatN  30665  osumcllem1N  30690  osumcllem9N  30698  pexmidlem6N  30709  dihmeetlem11N  32052  dochexmidlem6  32200
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 2416
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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ss 3326
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