Theorem zlmplusg

Description: Group operation of a ZZ -module. (Contributed by Mario Carneiro, 2-Oct-2015)

	Ref	Expression
Hypotheses	zlmbas.w	⊢ 𝑊 = ( ℤMod ‘ 𝐺 )
	zlmplusg.2	⊢ + = ( +g ‘ 𝐺 )
Assertion	zlmplusg	⊢ + = ( +g ‘ 𝑊 )

Proof

Step	Hyp	Ref	Expression
1		zlmbas.w	⊢ 𝑊 = ( ℤMod ‘ 𝐺 )
2		zlmplusg.2	⊢ + = ( +g ‘ 𝐺 )
3		df-plusg	⊢ +g = Slot 2
4		2nn	⊢ 2 ∈ ℕ
5		2lt5	⊢ 2 < 5
6	1 3 4 5	zlmlem	⊢ ( +g ‘ 𝐺 ) = ( +g ‘ 𝑊 )
7	2 6	eqtri	⊢ + = ( +g ‘ 𝑊 )