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Theorem releldmi 4915
Description: The first argument of a binary relation belongs to its domain. (Contributed by NM, 28-Apr-2015.)
Hypothesis
Ref Expression
releldm.1  |-  Rel  R
Assertion
Ref Expression
releldmi  |-  ( A R B  ->  A  e.  dom  R )

Proof of Theorem releldmi
StepHypRef Expression
1 releldm.1 . 2  |-  Rel  R
2 releldm 4911 . 2  |-  ( ( Rel  R  /\  A R B )  ->  A  e.  dom  R )
31, 2mpan 651 1  |-  ( A R B  ->  A  e.  dom  R )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   class class class wbr 4023   dom cdm 4689   Rel wrel 4694
This theorem is referenced by:  fpwwe2lem11  8262  fpwwe2lem12  8263  fpwwe2lem13  8264  rlimpm  11974  rlimdm  12025  iserex  12130  caucvgrlem2  12147  caucvgr  12148  caurcvg2  12150  caucvg  12151  fsumcvg3  12202  cvgcmpce  12276  climcnds  12310  trirecip  12321  ledm  14346  cmetcaulem  18714  ovoliunlem1  18861  mbflimlem  19022  dvaddf  19291  dvmulf  19292  dvcof  19297  dvcnv  19324  abelthlem5  19811  emcllem6  20294  hlimcaui  21816  stirlinglem12  27834
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-xp 4695  df-rel 4696  df-dm 4699
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