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	⊢ ( + ∈ 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 ∈ ℕ
5	1 2 3 4	2strop	⊢ ( + ∈ 𝑉 → + = ( +g ‘ 𝐺 ) )