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Theorem relssi 5099
Description: Inference from subclass principle for relations. (Contributed by NM, 31-Mar-1998.)
Hypotheses
Ref Expression
relssi.1
relssi.2
Assertion
Ref Expression
relssi
Distinct variable groups:   , ,   , ,

Proof of Theorem relssi
StepHypRef Expression
1 relssi.1 . . 3
2 ssrel 5096 . . 3
31, 2ax-mp 5 . 2
4 relssi.2 . . 3
54ax-gen 1618 . 2
63, 5mpgbir 1622 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:  xpsspwOLD  5122  oprssdm  6456  resiexg  6736  dftpos4  6993  enssdom  7560  idssen  7580  txuni2  20066  txpss3v  29528  pprodss4v  29534  aoprssdm  32287
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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