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Theorem imacnvcnv 4812
 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 4810 . . 3 (𝐴𝐵) = (𝐴𝐵)
21rneqi 4589 . 2 ran (𝐴𝐵) = ran (𝐴𝐵)
3 df-ima 4385 . 2 (𝐴𝐵) = ran (𝐴𝐵)
4 df-ima 4385 . 2 (𝐴𝐵) = ran (𝐴𝐵)
52, 3, 43eqtr4i 2086 1 (𝐴𝐵) = (𝐴𝐵)
 Colors of variables: wff set class Syntax hints:   = wceq 1259  ◡ccnv 4371  ran crn 4373   ↾ cres 4374   “ cima 4375 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3902  ax-pow 3954  ax-pr 3971 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-un 2949  df-in 2951  df-ss 2958  df-pw 3388  df-sn 3408  df-pr 3409  df-op 3411  df-br 3792  df-opab 3846  df-xp 4378  df-rel 4379  df-cnv 4380  df-dm 4382  df-rn 4383  df-res 4384  df-ima 4385 This theorem is referenced by: (None)
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