Theorem opprbas

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

	Ref	Expression
Hypotheses	opprbas.1	$$⊢O={opp}_r\left(R\right)$$
	opprbas.2	$$⊢B={\mathrm{Base}}_R$$
Assertion	opprbas	$$⊢B={\mathrm{Base}}_O$$

Proof

Step	Hyp	Ref	Expression
1		opprbas.1	$$⊢O={opp}_r\left(R\right)$$
2		opprbas.2	$$⊢B={\mathrm{Base}}_R$$
3		df-base	$$⊢\mathrm{Base}=\mathrm{Slot}1$$
4		1nn	$$⊢1\in \mathbb{N}$$
5		1lt3	$$⊢1<3$$
6	1 3 4 5	opprlem	$$⊢{\mathrm{Base}}_R={\mathrm{Base}}_O$$
7	2 6	eqtri	$$⊢B={\mathrm{Base}}_O$$