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Theorem tlmtrg 18211
 Description: The scalar ring of a topological module is a topological ring. (Contributed by Mario Carneiro, 5-Oct-2015.)
Hypothesis
Ref Expression
tlmtrg.f Scalar
Assertion
Ref Expression
tlmtrg TopMod

Proof of Theorem tlmtrg
StepHypRef Expression
1 eqid 2435 . . . 4
2 eqid 2435 . . . 4
3 tlmtrg.f . . . 4 Scalar
4 eqid 2435 . . . 4
51, 2, 3, 4istlm 18206 . . 3 TopMod TopMnd
65simplbi 447 . 2 TopMod TopMnd
76simp3d 971 1 TopMod
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 936   wceq 1652   wcel 1725  cfv 5446  (class class class)co 6073  Scalarcsca 13524  ctopn 13641  clmod 15942  cscaf 15943   ccn 17280   ctx 17584  TopMndctmd 18092  ctrg 18177  TopModctlm 18179 This theorem is referenced by:  tlmscatps  18212 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076  df-tlm 18183
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