ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rncnvcnv GIF version

Theorem rncnvcnv 4867
Description: The range of the double converse of a class. (Contributed by NM, 8-Apr-2007.)
Assertion
Ref Expression
rncnvcnv ran 𝐴 = ran 𝐴

Proof of Theorem rncnvcnv
StepHypRef Expression
1 df-rn 4652 . 2 ran 𝐴 = dom 𝐴
2 dfdm4 4834 . 2 dom 𝐴 = ran 𝐴
31, 2eqtr2i 2211 1 ran 𝐴 = ran 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1364  ccnv 4640  dom cdm 4641  ran crn 4642
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-pow 4189  ax-pr 4224
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-pw 3592  df-sn 3613  df-pr 3614  df-op 3616  df-br 4019  df-opab 4080  df-cnv 4649  df-dm 4651  df-rn 4652
This theorem is referenced by:  rnresv  5103
  Copyright terms: Public domain W3C validator