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Theorem releldmi 4895
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 4891 . 2  |-  ( ( Rel  R  /\  A R B )  ->  A  e.  dom  R )
31, 2mpan 424 1  |-  ( A R B  ->  A  e.  dom  R )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2164   class class class wbr 4029   dom cdm 4655   Rel wrel 4660
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2167  ax-ext 2175  ax-sep 4147  ax-pow 4203  ax-pr 4238
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477  df-rex 2478  df-v 2762  df-un 3157  df-in 3159  df-ss 3166  df-pw 3603  df-sn 3624  df-pr 3625  df-op 3627  df-br 4030  df-opab 4091  df-xp 4661  df-rel 4662  df-dm 4665
This theorem is referenced by:  iserex  11472  climrecvg1n  11481  climcvg1nlem  11482  fsum3cvg3  11529  trirecip  11634
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