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Theorem tdrgtps 22785
Description: A topological division ring is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
tdrgtps (𝑅 ∈ TopDRing → 𝑅 ∈ TopSp)

Proof of Theorem tdrgtps
StepHypRef Expression
1 tdrgtrg 22781 . 2 (𝑅 ∈ TopDRing → 𝑅 ∈ TopRing)
2 trgtps 22778 . 2 (𝑅 ∈ TopRing → 𝑅 ∈ TopSp)
31, 2syl 17 1 (𝑅 ∈ TopDRing → 𝑅 ∈ TopSp)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2112  TopSpctps 21540  TopRingctrg 22764  TopDRingctdrg 22765
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773  ax-nul 5177
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2601  df-eu 2632  df-clab 2780  df-cleq 2794  df-clel 2873  df-nfc 2941  df-ral 3114  df-rex 3115  df-rab 3118  df-v 3446  df-sbc 3724  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4247  df-sn 4529  df-pr 4531  df-op 4535  df-uni 4804  df-br 5034  df-iota 6287  df-fv 6336  df-ov 7142  df-tmd 22680  df-tgp 22681  df-trg 22768  df-tdrg 22769
This theorem is referenced by:  invrcn  22789  dvrcn  22792
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