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Theorem releldmi 5106
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 5102 . 2  |-  ( ( Rel  R  /\  A R B )  ->  A  e.  dom  R )
31, 2mpan 652 1  |-  ( A R B  ->  A  e.  dom  R )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   class class class wbr 4212   dom cdm 4878   Rel wrel 4883
This theorem is referenced by:  fpwwe2lem11  8515  fpwwe2lem12  8516  fpwwe2lem13  8517  rlimpm  12294  rlimdm  12345  iserex  12450  caucvgrlem2  12468  caucvgr  12469  caurcvg2  12471  caucvg  12472  fsumcvg3  12523  cvgcmpce  12597  climcnds  12631  trirecip  12642  ledm  14669  cmetcaulem  19241  ovoliunlem1  19398  mbflimlem  19559  dvaddf  19828  dvmulf  19829  dvcof  19834  dvcnv  19861  abelthlem5  20351  emcllem6  20839  hlimcaui  22739  lgamgulmlem4  24816  stirlinglem12  27810  rlimdmafv  28017
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-xp 4884  df-rel 4885  df-dm 4888
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