Metamath Proof Explorer


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