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Theorem breldmg 4791
 Description: Membership of first of a binary relation in a domain. (Contributed by NM, 21-Mar-2007.)
Assertion
Ref Expression
breldmg

Proof of Theorem breldmg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 breq2 3969 . . . . 5
21spcegv 2800 . . . 4
32imp 123 . . 3
433adant1 1000 . 2
5 eldmg 4780 . . 3
653ad2ant1 1003 . 2
74, 6mpbird 166 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   w3a 963  wex 1472   wcel 2128   class class class wbr 3965   cdm 4585 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567  df-op 3569  df-br 3966  df-dm 4595 This theorem is referenced by:  brelrng  4816  releldm  4820  brtposg  6198  shftfvalg  10711  shftfval  10714  geolim2  11402  geoisum1c  11410  ntrivcvgap  11438  eftlub  11580  eflegeo  11591  dvcj  13044  dvrecap  13048  dvef  13059  trilpolemisumle  13580  trilpolemeq1  13582
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