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Theorem imacnvcnv 4998
Description: The image of the double converse of a class. (Contributed by NM, 8-Apr-2007.)
Assertion
Ref Expression
imacnvcnv (𝐴𝐵) = (𝐴𝐵)

Proof of Theorem imacnvcnv
StepHypRef Expression
1 rescnvcnv 4996 . . 3 (𝐴𝐵) = (𝐴𝐵)
21rneqi 4762 . 2 ran (𝐴𝐵) = ran (𝐴𝐵)
3 df-ima 4547 . 2 (𝐴𝐵) = ran (𝐴𝐵)
4 df-ima 4547 . 2 (𝐴𝐵) = ran (𝐴𝐵)
52, 3, 43eqtr4i 2168 1 (𝐴𝐵) = (𝐴𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1331  ccnv 4533  ran crn 4535  cres 4536  cima 4537
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 2119  ax-sep 4041  ax-pow 4093  ax-pr 4126
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-opab 3985  df-xp 4540  df-rel 4541  df-cnv 4542  df-dm 4544  df-rn 4545  df-res 4546  df-ima 4547
This theorem is referenced by:  casedm  6964  caseinl  6969  caseinr  6970  djudm  6983  hmeoima  12468  hmeocld  12470  hmeontr  12471
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