Theorem crngmgp

Description: A commutative ring's multiplication operation is commutative. (Contributed by Mario Carneiro, 7-Jan-2015)

	Ref	Expression
Hypothesis	ringmgp.g	|- G = ( mulGrp ` R )
Assertion	crngmgp	|- ( R e. CRing -> G e. CMnd )

Proof

Step	Hyp	Ref	Expression
1		ringmgp.g	|- G = ( mulGrp ` R )
2	1	iscrng	|- ( R e. CRing <-> ( R e. Ring /\ G e. CMnd ) )
3	2	simprbi	|- ( R e. CRing -> G e. CMnd )