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Theorem releldmi 5060
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 5056 . 2  |-  ( ( Rel  R  /\  A R B )  ->  A  e.  dom  R )
31, 2mpan 668 1  |-  ( A R B  ->  A  e.  dom  R )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1842   class class class wbr 4395   dom cdm 4823   Rel wrel 4828
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4517  ax-nul 4525  ax-pr 4630
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-rab 2763  df-v 3061  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-br 4396  df-opab 4454  df-xp 4829  df-rel 4830  df-dm 4833
This theorem is referenced by:  fpwwe2lem11  9048  fpwwe2lem12  9049  fpwwe2lem13  9050  rlimpm  13472  rlimdm  13523  iserex  13628  caucvgrlem2  13646  caucvgr  13647  caurcvg2  13649  caucvg  13650  fsumcvg3  13700  cvgcmpce  13783  climcnds  13814  trirecip  13826  ledm  16178  cmetcaulem  22019  ovoliunlem1  22205  mbflimlem  22366  dvaddf  22637  dvmulf  22638  dvcof  22643  dvcnv  22670  abelthlem5  23122  emcllem6  23656  lgamgulmlem4  23687  hlimcaui  26568  brfvrcld2  35671  sumnnodd  37004  stirlinglem12  37235  fouriersw  37382  rlimdmafv  37630
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