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Theorem tdrgrng 18125
Description: A topological division ring is a ring. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
tdrgrng  |-  ( R  e. TopDRing  ->  R  e.  Ring )

Proof of Theorem tdrgrng
StepHypRef Expression
1 tdrgtrg 18123 . 2  |-  ( R  e. TopDRing  ->  R  e.  TopRing )
2 trgrng 18121 . 2  |-  ( R  e.  TopRing  ->  R  e.  Ring )
31, 2syl 16 1  |-  ( R  e. TopDRing  ->  R  e.  Ring )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1717   Ringcrg 15587   TopRingctrg 18106  TopDRingctdrg 18107
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-rex 2655  df-rab 2658  df-v 2901  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-uni 3958  df-br 4154  df-iota 5358  df-fv 5402  df-ov 6023  df-trg 18110  df-tdrg 18111
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