Theorem grpidcl

Description: The identity element of a group belongs to the group. (Contributed by NM, 27-Aug-2011) (Revised by Mario Carneiro, 27-Dec-2014)

	Ref	Expression
Hypotheses	grpidcl.b	|- B = ( Base ` G )
	grpidcl.o	|- .0. = ( 0g ` G )
Assertion	grpidcl	|- ( G e. Grp -> .0. e. B )

Proof

Step	Hyp	Ref	Expression
1		grpidcl.b	|- B = ( Base ` G )
2		grpidcl.o	|- .0. = ( 0g ` G )
3		grpmnd	|- ( G e. Grp -> G e. Mnd )
4	1 2	mndidcl	|- ( G e. Mnd -> .0. e. B )
5	3 4	syl	|- ( G e. Grp -> .0. e. B )