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Theorem imacnvcnv 5634
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 5632 . . 3 (𝐴𝐵) = (𝐴𝐵)
21rneqi 5384 . 2 ran (𝐴𝐵) = ran (𝐴𝐵)
3 df-ima 5156 . 2 (𝐴𝐵) = ran (𝐴𝐵)
4 df-ima 5156 . 2 (𝐴𝐵) = ran (𝐴𝐵)
52, 3, 43eqtr4i 2683 1 (𝐴𝐵) = (𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1523  ccnv 5142  ran crn 5144  cres 5145  cima 5146
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814  ax-nul 4822  ax-pr 4936
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-eu 2502  df-mo 2503  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-br 4686  df-opab 4746  df-xp 5149  df-rel 5150  df-cnv 5151  df-dm 5153  df-rn 5154  df-res 5155  df-ima 5156
This theorem is referenced by:  curry1  7314  curry2  7317  fnwelem  7337  fpwwe2lem6  9495  fpwwe2lem9  9498  eqglact  17692  hmeoima  21616  hmeocld  21618  hmeocls  21619  hmeontr  21620  reghmph  21644  qtopf1  21667  tgpconncompeqg  21962  imasf1obl  22340  mbfimaopnlem  23467  hmeoclda  32453
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