Theorem grpplusgOLD

Description: Obsolete version of grpplusg as of 27-Oct-2024. The operation of a constructed group. (Contributed by Mario Carneiro, 2-Aug-2013) (Revised by Mario Carneiro, 30-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	grpfn.g	|- G = { <. ( Base ` ndx ) , B >. , <. ( +g ` ndx ) , .+ >. }
Assertion	grpplusgOLD	|- ( .+ e. V -> .+ = ( +g ` G ) )

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	2strop	|- ( .+ e. V -> .+ = ( +g ` G ) )