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Theorem releldmi 4674
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 (𝐴𝑅𝐵𝐴 ∈ dom 𝑅)

Proof of Theorem releldmi
StepHypRef Expression
1 releldm.1 . 2 Rel 𝑅
2 releldm 4670 . 2 ((Rel 𝑅𝐴𝑅𝐵) → 𝐴 ∈ dom 𝑅)
31, 2mpan 415 1 (𝐴𝑅𝐵𝐴 ∈ dom 𝑅)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1438   class class class wbr 3845  dom cdm 4438  Rel wrel 4443
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3957  ax-pow 4009  ax-pr 4036
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-rex 2365  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-pw 3431  df-sn 3452  df-pr 3453  df-op 3455  df-br 3846  df-opab 3900  df-xp 4444  df-rel 4445  df-dm 4448
This theorem is referenced by:  iserex  10727  climrecvg1n  10737  climcvg1nlem  10738  fsum3cvg3  10789  trirecip  10895
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