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Theorem rncnvcnv 5886
Description: The range of the double converse of a class is equal to its range (even when that class in not a relation). (Contributed by NM, 8-Apr-2007.)
Assertion
Ref Expression
rncnvcnv ran 𝐴 = ran 𝐴

Proof of Theorem rncnvcnv
StepHypRef Expression
1 df-rn 5642 . 2 ran 𝐴 = dom 𝐴
2 dfdm4 5848 . 2 dom 𝐴 = ran 𝐴
31, 2eqtr2i 2767 1 ran 𝐴 = ran 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  ccnv 5630  dom cdm 5631  ran crn 5632
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2709  ax-sep 5255  ax-nul 5262  ax-pr 5383
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3407  df-v 3446  df-dif 3912  df-un 3914  df-in 3916  df-ss 3926  df-nul 4282  df-if 4486  df-sn 4586  df-pr 4588  df-op 4592  df-br 5105  df-opab 5167  df-cnv 5639  df-dm 5641  df-rn 5642
This theorem is referenced by:  rnresv  6150  trrelsuperrel2dg  41742
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