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Theorem tdrgtps 18237
Description: A topological division ring is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
tdrgtps  |-  ( R  e. TopDRing  ->  R  e.  TopSp )

Proof of Theorem tdrgtps
StepHypRef Expression
1 tdrgtrg 18233 . 2  |-  ( R  e. TopDRing  ->  R  e.  TopRing )
2 trgtps 18230 . 2  |-  ( R  e.  TopRing  ->  R  e.  TopSp )
31, 2syl 16 1  |-  ( R  e. TopDRing  ->  R  e.  TopSp )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1727   TopSpctps 16992   TopRingctrg 18216  TopDRingctdrg 18217
This theorem is referenced by:  invrcn  18241  dvrcn  18244
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-nul 4363
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-sbc 3168  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-iota 5447  df-fv 5491  df-ov 6113  df-tmd 18133  df-tgp 18134  df-trg 18220  df-tdrg 18221
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