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Theorem trgtmd 19870
 Description: The multiplicative monoid of a topological ring is a topological monoid. (Contributed by Mario Carneiro, 5-Oct-2015.)
Hypothesis
Ref Expression
istrg.1 mulGrp
Assertion
Ref Expression
trgtmd TopMnd

Proof of Theorem trgtmd
StepHypRef Expression
1 istrg.1 . . 3 mulGrp
21istrg 19869 . 2 TopMnd
32simp3bi 1005 1 TopMnd
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1370   wcel 1758  cfv 5525  mulGrpcmgp 16712  crg 16767  TopMndctmd 19772  ctgp 19773  ctrg 19861 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 1955  ax-ext 2432 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 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rex 2804  df-rab 2807  df-v 3078  df-dif 3438  df-un 3440  df-in 3442  df-ss 3449  df-nul 3745  df-if 3899  df-sn 3985  df-pr 3987  df-op 3991  df-uni 4199  df-br 4400  df-iota 5488  df-fv 5533  df-trg 19865 This theorem is referenced by:  mulrcn  19884  cnmpt1mulr  19887  cnmpt2mulr  19888  nrgtdrg  20404  iistmd  26476
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