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Theorem relssi 5002
 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 4999 . . 3
31, 2ax-mp 5 . 2
4 relssi.2 . . 3
54ax-gen 1556 . 2
63, 5mpgbir 1560 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550   wcel 1728   wss 3309  cop 3846   wrel 4918 This theorem is referenced by:  xpsspwOLD  5022  resiexg  5223  oprssdm  6264  dftpos4  6534  enssdom  7168  idssen  7188  txuni2  17635  txpss3v  25758  pprodss4v  25764  aoprssdm  28154 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4361  ax-nul 4369  ax-pr 4438 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3768  df-sn 3849  df-pr 3850  df-op 3852  df-opab 4298  df-xp 4919  df-rel 4920
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