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

Theorem dmcnvcnv 4763
 Description: The domain of the double converse of a class (which doesn't have to be a relation as in dfrel2 4989). (Contributed by NM, 8-Apr-2007.)
Assertion
Ref Expression
dmcnvcnv

Proof of Theorem dmcnvcnv
StepHypRef Expression
1 dfdm4 4731 . 2
2 df-rn 4550 . 2
31, 2eqtr2i 2161 1
 Colors of variables: wff set class Syntax hints:   wceq 1331  ccnv 4538   cdm 4539   crn 4540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-cnv 4547  df-dm 4549  df-rn 4550 This theorem is referenced by:  resdm2  5029  f1cnvcnv  5339
 Copyright terms: Public domain W3C validator