Theorem opprbas

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

	Ref	Expression
Hypotheses	opprbas.1	|- O = ( oppR ` R )
	opprbas.2	|- B = ( Base ` R )
Assertion	opprbas	|- B = ( Base ` O )

Proof

Step	Hyp	Ref	Expression
1		opprbas.1	|- O = ( oppR ` R )
2		opprbas.2	|- B = ( Base ` R )
3		df-base	|- Base = Slot 1
4		1nn	|- 1 e. NN
5		1lt3	|- 1 < 3
6	1 3 4 5	opprlem	|- ( Base ` R ) = ( Base ` O )
7	2 6	eqtri	|- B = ( Base ` O )