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Theorem rncnv 36750
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 5850 . 2 dom 𝐴 = ran 𝐴
21eqcomi 2745 1 ran 𝐴 = dom 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  ccnv 5631  dom cdm 5632  ran crn 5633
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707  ax-sep 5255  ax-nul 5262  ax-pr 5383
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3407  df-v 3446  df-dif 3912  df-un 3914  df-in 3916  df-ss 3926  df-nul 4282  df-if 4486  df-sn 4586  df-pr 4588  df-op 4592  df-br 5105  df-opab 5167  df-cnv 5640  df-dm 5642  df-rn 5643
This theorem is referenced by:  dmcoss3  36904  symrelim  37010  symrefref2  37014
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