Theorem tdrgtps 24092

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 24088	. 2 ⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopRing)
2		trgtps 24085	. 2 ⊢ (𝑅 ∈ TopRing → 𝑅 ∈ TopSp)
3	1, 2	syl 17	1 ⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopSp)

Syntax hints:   → wi 4   ∈ wcel 2111  TopSpctps 22847  TopRingctrg 24071  TopDRingctdrg 24072

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 2113  ax-9 2121  ax-ext 2703  ax-nul 5242

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 2710  df-cleq 2723  df-clel 2806  df-ne 2929  df-rab 3396  df-v 3438  df-sbc 3737  df-dif 3900  df-un 3902  df-in 3904  df-ss 3914  df-nul 4281  df-if 4473  df-sn 4574  df-pr 4576  df-op 4580  df-uni 4857  df-br 5090  df-iota 6437  df-fv 6489  df-ov 7349  df-tmd 23987  df-tgp 23988  df-trg 24075  df-tdrg 24076

This theorem is referenced by:  invrcn  24096  dvrcn  24099