Theorem oppradd

Description: Addition operation of an opposite ring. (Contributed by Mario Carneiro, 1-Dec-2014)

	Ref	Expression
Hypotheses	opprbas.1	⊢ 𝑂 = ( oppr ‘ 𝑅 )
	oppradd.2	⊢ + = ( +g ‘ 𝑅 )
Assertion	oppradd	⊢ + = ( +g ‘ 𝑂 )

Proof

Step	Hyp	Ref	Expression
1		opprbas.1	⊢ 𝑂 = ( oppr ‘ 𝑅 )
2		oppradd.2	⊢ + = ( +g ‘ 𝑅 )
3		df-plusg	⊢ +g = Slot 2
4		2nn	⊢ 2 ∈ ℕ
5		2lt3	⊢ 2 < 3
6	1 3 4 5	opprlem	⊢ ( +g ‘ 𝑅 ) = ( +g ‘ 𝑂 )
7	2 6	eqtri	⊢ + = ( +g ‘ 𝑂 )