Metamath Proof Explorer


Theorem grpbase

Description: The base set of a constructed group. (Contributed by Mario Carneiro, 2-Aug-2013) (Revised by Mario Carneiro, 30-Apr-2015)

Ref Expression
Hypothesis grpfn.g 𝐺 = { ⟨ ( Base ‘ ndx ) , 𝐵 ⟩ , ⟨ ( +g ‘ ndx ) , + ⟩ }
Assertion grpbase ( 𝐵𝑉𝐵 = ( Base ‘ 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 2strbas ( 𝐵𝑉𝐵 = ( Base ‘ 𝐺 ) )