Database
BASIC TOPOLOGY
Filters and filter bases
Topological rings, fields, vector spaces
trgring
Next ⟩
trggrp
Metamath Proof Explorer
Ascii
Unicode
Theorem
trgring
Description:
A topological ring is a ring.
(Contributed by
Mario Carneiro
, 5-Oct-2015)
Ref
Expression
Assertion
trgring
⊢
R
∈
TopRing
→
R
∈
Ring
Proof
Step
Hyp
Ref
Expression
1
eqid
⊢
mulGrp
R
=
mulGrp
R
2
1
istrg
⊢
R
∈
TopRing
↔
R
∈
TopGrp
∧
R
∈
Ring
∧
mulGrp
R
∈
TopMnd
3
2
simp2bi
⊢
R
∈
TopRing
→
R
∈
Ring