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Theorem tdrgtps 18072
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 18068 . 2  |-  ( R  e. TopDRing  ->  R  e.  TopRing )
2 trgtps 18065 . 2  |-  ( R  e.  TopRing  ->  R  e.  TopSp )
31, 2syl 15 1  |-  ( R  e. TopDRing  ->  R  e.  TopSp )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1715   TopSpctps 16851   TopRingctrg 18051  TopDRingctdrg 18052
This theorem is referenced by:  invrcn  18076  dvrcn  18079
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347  ax-nul 4251
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 937  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-eu 2221  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-ne 2531  df-ral 2633  df-rex 2634  df-rab 2637  df-v 2875  df-sbc 3078  df-dif 3241  df-un 3243  df-in 3245  df-ss 3252  df-nul 3544  df-if 3655  df-sn 3735  df-pr 3736  df-op 3738  df-uni 3930  df-br 4126  df-iota 5322  df-fv 5366  df-ov 5984  df-tmd 17968  df-tgp 17969  df-trg 18055  df-tdrg 18056
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