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Theorem releldmi 4778
 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 4774 . 2 ((Rel 𝑅𝐴𝑅𝐵) → 𝐴 ∈ dom 𝑅)
31, 2mpan 420 1 (𝐴𝑅𝐵𝐴 ∈ dom 𝑅)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1480   class class class wbr 3929  dom cdm 4539  Rel wrel 4544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-xp 4545  df-rel 4546  df-dm 4549 This theorem is referenced by:  iserex  11115  climrecvg1n  11124  climcvg1nlem  11125  fsum3cvg3  11172  trirecip  11277
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