Theorem tdrgtps 24119

Description: A topological division ring is a topological space. (Contributed by Mario Carneiro, 5-Oct-2015.)

Assertion

Ref	Expression
tdrgtps	⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopSp)

Proof of Theorem tdrgtps

Step	Hyp	Ref	Expression
1		tdrgtrg 24115	. 2 ⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopRing)
2		trgtps 24112	. 2 ⊢ (𝑅 ∈ TopRing → 𝑅 ∈ TopSp)
3	1, 2	syl 17	1 ⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopSp)

Syntax hints:   → wi 4   ∈ wcel 2113  TopSpctps 22874  TopRingctrg 24098  TopDRingctdrg 24099

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2706  ax-nul 5249

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-ne 2931  df-rab 3398  df-v 3440  df-sbc 3739  df-dif 3902  df-un 3904  df-in 3906  df-ss 3916  df-nul 4284  df-if 4478  df-sn 4579  df-pr 4581  df-op 4585  df-uni 4862  df-br 5097  df-iota 6446  df-fv 6498  df-ov 7359  df-tmd 24014  df-tgp 24015  df-trg 24102  df-tdrg 24103

This theorem is referenced by:  invrcn  24123  dvrcn  24126