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Theorem dmcnvcnv 4772
 Description: The domain of the double converse of a class (which doesn't have to be a relation as in dfrel2 4998). (Contributed by NM, 8-Apr-2007.)
Assertion
Ref Expression
dmcnvcnv dom 𝐴 = dom 𝐴

Proof of Theorem dmcnvcnv
StepHypRef Expression
1 dfdm4 4740 . 2 dom 𝐴 = ran 𝐴
2 df-rn 4559 . 2 ran 𝐴 = dom 𝐴
31, 2eqtr2i 2162 1 dom 𝐴 = dom 𝐴
 Colors of variables: wff set class Syntax hints:   = wceq 1332  ◡ccnv 4547  dom cdm 4548  ran crn 4549 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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4055  ax-pow 4107  ax-pr 4140 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-un 3081  df-in 3083  df-ss 3090  df-pw 3518  df-sn 3539  df-pr 3540  df-op 3542  df-br 3939  df-opab 3999  df-cnv 4556  df-dm 4558  df-rn 4559 This theorem is referenced by:  resdm2  5038  f1cnvcnv  5348
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