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Theorem dmcnvcnv 4586
Description: The domain of the double converse of a class (which doesn't have to be a relation as in dfrel2 4801). (Contributed by NM, 8-Apr-2007.)
Assertion
Ref Expression
dmcnvcnv  |-  dom  `' `' A  =  dom  A

Proof of Theorem dmcnvcnv
StepHypRef Expression
1 dfdm4 4555 . 2  |-  dom  A  =  ran  `' A
2 df-rn 4382 . 2  |-  ran  `' A  =  dom  `' `' A
31, 2eqtr2i 2103 1  |-  dom  `' `' A  =  dom  A
Colors of variables: wff set class
Syntax hints:    = wceq 1285   `'ccnv 4370   dom cdm 4371   ran crn 4372
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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-cnv 4379  df-dm 4381  df-rn 4382
This theorem is referenced by:  resdm2  4841  f1cnvcnv  5131
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