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Theorem errn 7119
 Description: The range and domain of an equivalence relation are equal. (Contributed by Rodolfo Medina, 11-Oct-2010.) (Revised by Mario Carneiro, 12-Aug-2015.)
Assertion
Ref Expression
errn

Proof of Theorem errn
StepHypRef Expression
1 df-rn 4847 . 2
2 ercnv 7118 . . . 4
32dmeqd 5038 . . 3
4 erdm 7107 . . 3
53, 4eqtrd 2473 . 2
61, 5syl5eq 2485 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1364  ccnv 4835   cdm 4836   crn 4837   wer 7094 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-9 1765  ax-10 1780  ax-11 1785  ax-12 1797  ax-13 1948  ax-ext 2422  ax-sep 4410  ax-nul 4418  ax-pr 4528 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 962  df-tru 1367  df-ex 1592  df-nf 1595  df-sb 1706  df-eu 2261  df-mo 2262  df-clab 2428  df-cleq 2434  df-clel 2437  df-nfc 2566  df-ne 2606  df-ral 2718  df-rex 2719  df-rab 2722  df-v 2972  df-dif 3328  df-un 3330  df-in 3332  df-ss 3339  df-nul 3635  df-if 3789  df-sn 3875  df-pr 3877  df-op 3881  df-br 4290  df-opab 4348  df-xp 4842  df-rel 4843  df-cnv 4844  df-dm 4846  df-rn 4847  df-er 7097 This theorem is referenced by:  erssxp  7120  ecss  7138  uniqs2  7158  sylow2a  16111
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