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Theorem releldmi 4746
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 4742 . 2  |-  ( ( Rel  R  /\  A R B )  ->  A  e.  dom  R )
31, 2mpan 418 1  |-  ( A R B  ->  A  e.  dom  R )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1463   class class class wbr 3897   dom cdm 4507   Rel wrel 4512
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-14 1475  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-sep 4014  ax-pow 4066  ax-pr 4099
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-rex 2397  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-pw 3480  df-sn 3501  df-pr 3502  df-op 3504  df-br 3898  df-opab 3958  df-xp 4513  df-rel 4514  df-dm 4517
This theorem is referenced by:  iserex  11048  climrecvg1n  11057  climcvg1nlem  11058  fsum3cvg3  11105  trirecip  11210
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