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Theorem relssdv 5100
Description: Deduction from subclass principle for relations. (Contributed by NM, 11-Sep-2004.)
Hypotheses
Ref Expression
relssdv.1
relssdv.2
Assertion
Ref Expression
relssdv
Distinct variable groups:   , ,   , ,   , ,

Proof of Theorem relssdv
StepHypRef Expression
1 relssdv.2 . . 3
21alrimivv 1720 . 2
3 relssdv.1 . . 3
4 ssrel 5096 . . 3
53, 4syl 16 . 2
62, 5mpbird 232 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  e.wcel 1818  C_wss 3475  <.cop 4035  Relwrel 5009
This theorem is referenced by:  relssres  5316  poirr2  5396  sofld  5460  relssdmrn  5533  funcres2  15267  wunfunc  15268  fthres2  15301  pospo  15603  joindmss  15637  meetdmss  15651  clatl  15746  subrgdvds  17443  opsrtoslem2  18149  txcls  20105  txdis1cn  20136  txkgen  20153  qustgplem  20619  metustidOLD  21062  metustid  21063  metustexhalfOLD  21066  metustexhalf  21067  ovoliunlem1  21913  dvres2  22316  cvmlift2lem12  28759  dib2dim  36970  dih2dimbALTN  36972  dihmeetlem1N  37017  dihglblem5apreN  37018  dihmeetlem13N  37046  dihjatcclem4  37148
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  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-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010  df-rel 5011
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