Theorem tdrgtmd 24089

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

Assertion

Ref	Expression
tdrgtmd	⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopMnd)

Proof of Theorem tdrgtmd

Step	Hyp	Ref	Expression
1		tdrgtrg 24086	. 2 ⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopRing)
2		trgtmd2 24082	. 2 ⊢ (𝑅 ∈ TopRing → 𝑅 ∈ TopMnd)
3	1, 2	syl 17	1 ⊢ (𝑅 ∈ TopDRing → 𝑅 ∈ TopMnd)

Syntax hints:   → wi 4   ∈ wcel 2111  TopMndctmd 23983  TopRingctrg 24069  TopDRingctdrg 24070

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 5244

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 3742  df-dif 3905  df-un 3907  df-in 3909  df-ss 3919  df-nul 4284  df-if 4476  df-sn 4577  df-pr 4579  df-op 4583  df-uni 4860  df-br 5092  df-iota 6437  df-fv 6489  df-ov 7349  df-tgp 23986  df-trg 24073  df-tdrg 24074

This theorem is referenced by: (None)