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Theorem dmcnvcnv 5256
Description: The domain of the double converse of a class (which doesn't have to be a relation as in dfrel2 5488). (Contributed by NM, 8-Apr-2007.)
Assertion
Ref Expression
dmcnvcnv dom 𝐴 = dom 𝐴

Proof of Theorem dmcnvcnv
StepHypRef Expression
1 dfdm4 5225 . 2 dom 𝐴 = ran 𝐴
2 df-rn 5039 . 2 ran 𝐴 = dom 𝐴
31, 2eqtr2i 2632 1 dom 𝐴 = dom 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  ccnv 5027  dom cdm 5028  ran crn 5029
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589  ax-sep 4703  ax-nul 4712  ax-pr 4828
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-eu 2461  df-mo 2462  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-rab 2904  df-v 3174  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-br 4578  df-opab 4638  df-cnv 5036  df-dm 5038  df-rn 5039
This theorem is referenced by:  resdm2  5528  f1cnvcnv  6007  trrelsuperrel2dg  36778
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