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Theorem tdrgtmd 18119
Description: A topological division ring is a topological monoid. (Contributed by Mario Carneiro, 5-Oct-2015.)
Assertion
Ref Expression
tdrgtmd  |-  ( R  e. TopDRing  ->  R  e. TopMnd )

Proof of Theorem tdrgtmd
StepHypRef Expression
1 tdrgtrg 18116 . 2  |-  ( R  e. TopDRing  ->  R  e.  TopRing )
2 trgtmd2 18112 . 2  |-  ( R  e.  TopRing  ->  R  e. TopMnd )
31, 2syl 16 1  |-  ( R  e. TopDRing  ->  R  e. TopMnd )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1717  TopMndctmd 18014   TopRingctrg 18099  TopDRingctdrg 18100
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 2361  ax-nul 4272
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 2235  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-sbc 3098  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-uni 3951  df-br 4147  df-iota 5351  df-fv 5395  df-ov 6016  df-tgp 18017  df-trg 18103  df-tdrg 18104
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