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Theorem rncnv 35676
 Description: Range of converse is the domain. (Contributed by Peter Mazsa, 12-Feb-2018.)
Assertion
Ref Expression
rncnv ran 𝐴 = dom 𝐴

Proof of Theorem rncnv
StepHypRef Expression
1 dfdm4 5741 . 2 dom 𝐴 = ran 𝐴
21eqcomi 2831 1 ran 𝐴 = dom 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538  ◡ccnv 5531  dom cdm 5532  ran crn 5533 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794  ax-sep 5179  ax-nul 5186  ax-pr 5307 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2622  df-eu 2653  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-v 3471  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4266  df-if 4440  df-sn 4540  df-pr 4542  df-op 4546  df-br 5043  df-opab 5105  df-cnv 5540  df-dm 5542  df-rn 5543 This theorem is referenced by:  dmcoss3  35811  symrelim  35913  symrefref2  35917
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