Theorem tdrgtps 22307

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 22303	. 2 ⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopRing)
2		trgtps 22300	. 2 ⊢ (𝑅 ∈ TopRing → 𝑅 ∈ TopSp)
3	1, 2	syl 17	1 ⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopSp)

Syntax hints:   → wi 4   ∈ wcel 2157  TopSpctps 21064  TopRingctrg 22286  TopDRingctdrg 22287

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2378  ax-ext 2778  ax-nul 4984

This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-3an 1110  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-mo 2592  df-eu 2610  df-clab 2787  df-cleq 2793  df-clel 2796  df-nfc 2931  df-ral 3095  df-rex 3096  df-rab 3099  df-v 3388  df-sbc 3635  df-dif 3773  df-un 3775  df-in 3777  df-ss 3784  df-nul 4117  df-if 4279  df-sn 4370  df-pr 4372  df-op 4376  df-uni 4630  df-br 4845  df-iota 6065  df-fv 6110  df-ov 6882  df-tmd 22203  df-tgp 22204  df-trg 22290  df-tdrg 22291

This theorem is referenced by:  invrcn  22311  dvrcn  22314