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Theorem releldmi 4931
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 4927 . 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 1696   class class class wbr 4039   dom cdm 4705   Rel wrel 4710
This theorem is referenced by:  fpwwe2lem11  8278  fpwwe2lem12  8279  fpwwe2lem13  8280  rlimpm  11990  rlimdm  12041  iserex  12146  caucvgrlem2  12163  caucvgr  12164  caurcvg2  12166  caucvg  12167  fsumcvg3  12218  cvgcmpce  12292  climcnds  12326  trirecip  12337  ledm  14362  cmetcaulem  18730  ovoliunlem1  18877  mbflimlem  19038  dvaddf  19307  dvmulf  19308  dvcof  19313  dvcnv  19340  abelthlem5  19827  emcllem6  20310  hlimcaui  21832  stirlinglem12  27937  rlimdmafv  28145
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-xp 4711  df-rel 4712  df-dm 4715
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