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Theorem dmcnvcnv 5032
Description: The domain of the double converse of a class (which doesn't have to be a relation as in dfrel2 5261). (Contributed by NM, 8-Apr-2007.)
Assertion
Ref Expression
dmcnvcnv  |-  dom  `' `' A  =  dom  A

Proof of Theorem dmcnvcnv
StepHypRef Expression
1 dfdm4 5003 . 2  |-  dom  A  =  ran  `' A
2 df-rn 4829 . 2  |-  ran  `' A  =  dom  `' `' A
31, 2eqtr2i 2408 1  |-  dom  `' `' A  =  dom  A
Colors of variables: wff set class
Syntax hints:    = wceq 1649   `'ccnv 4817   dom cdm 4818   ran crn 4819
This theorem is referenced by:  resdm2  5300  f1cnvcnv  5587
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-sep 4271  ax-nul 4279  ax-pr 4344
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2242  df-mo 2243  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-br 4154  df-opab 4208  df-cnv 4826  df-dm 4828  df-rn 4829
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