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Theorem trgrng 19858
 Description: A topological ring is a ring. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
trgrng

Proof of Theorem trgrng
StepHypRef Expression
1 eqid 2451 . . 3 mulGrp mulGrp
21istrg 19851 . 2 mulGrp TopMnd
32simp2bi 1004 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1758  cfv 5513  mulGrpcmgp 16693  crg 16748  TopMndctmd 19754  ctgp 19755  ctrg 19843 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2599  df-rex 2799  df-rab 2802  df-v 3067  df-dif 3426  df-un 3428  df-in 3430  df-ss 3437  df-nul 3733  df-if 3887  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4187  df-br 4388  df-iota 5476  df-fv 5521  df-trg 19847 This theorem is referenced by:  trggrp  19859  tdrgrng  19862
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