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Theorem tdrgtmd 24098
Description: A topological division ring is a topological monoid. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
tdrgtmd (𝑅 ∈ TopDRing → 𝑅 ∈ TopMnd)

Proof of Theorem tdrgtmd
StepHypRef Expression
1 tdrgtrg 24095 . 2 (𝑅 ∈ TopDRing → 𝑅 ∈ TopRing)
2 trgtmd2 24091 . 2 (𝑅 ∈ TopRing → 𝑅 ∈ TopMnd)
31, 2syl 17 1 (𝑅 ∈ TopDRing → 𝑅 ∈ TopMnd)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  TopMndctmd 23992  TopRingctrg 24078  TopDRingctdrg 24079
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698  ax-nul 5308
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-ne 2937  df-rab 3429  df-v 3473  df-sbc 3777  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4325  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4911  df-br 5151  df-iota 6503  df-fv 6559  df-ov 7427  df-tgp 23995  df-trg 24082  df-tdrg 24083
This theorem is referenced by: (None)
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