Theorem tdrgtps 24511

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 24507	. 2 ⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopRing)
2		trgtps 24504	. 2 ⊢ (𝑅 ∈ TopRing → 𝑅 ∈ TopSp)
3	1, 2	syl 18	1 ⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopSp)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2146  TopSpctps 23265  TopRingctrg 24490  TopDRingctdrg 24491

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735  ax-nul 5263

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2839  df-ne 2960  df-rab 3417  df-v 3456  df-sbc 3743  df-ss 3901  df-dif 4050  df-in 4094  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4839  df-uni 4871  df-br 5107  df-iota 6501  df-fv 6555  df-ov 7433  df-tmd 24406  df-tgp 24407  df-trg 24494  df-tdrg 24495

This theorem is used by:  invrcn  24515  dvrcn  24518