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Theorem tdrgtps 18163
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 18159 . 2  |-  ( R  e. TopDRing  ->  R  e.  TopRing )
2 trgtps 18156 . 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 1721   TopSpctps 16920   TopRingctrg 18142  TopDRingctdrg 18143
This theorem is referenced by:  invrcn  18167  dvrcn  18170
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 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389  ax-nul 4302
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-eu 2262  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-ral 2675  df-rex 2676  df-rab 2679  df-v 2922  df-sbc 3126  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-op 3787  df-uni 3980  df-br 4177  df-iota 5381  df-fv 5425  df-ov 6047  df-tmd 18059  df-tgp 18060  df-trg 18146  df-tdrg 18147
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