Theorem grpstr

Description: A constructed group is a structure on 1 ... 2 . (Contributed by Mario Carneiro, 28-Sep-2013) (Revised by Mario Carneiro, 30-Apr-2015)

	Ref	Expression
Hypothesis	grpfn.g	|- G = { <. ( Base ` ndx ) , B >. , <. ( +g ` ndx ) , .+ >. }
Assertion	grpstr	|- G Struct <. 1 , 2 >.

Proof

Step	Hyp	Ref	Expression
1		grpfn.g	|- G = { <. ( Base ` ndx ) , B >. , <. ( +g ` ndx ) , .+ >. }
2		df-plusg	|- +g = Slot 2
3		1lt2	|- 1 < 2
4		2nn	|- 2 e. NN
5	1 2 3 4	2strstr	|- G Struct <. 1 , 2 >.