Theorem ridl1

Description: Every ring contains a unit right ideal. (Contributed by AV, 13-Feb-2025)

	Ref	Expression
Hypotheses	ridl0.u	|- U = ( LIdeal ` ( oppR ` R ) )
	ridl1.b	|- B = ( Base ` R )
Assertion	ridl1	|- ( R e. Ring -> B e. U )

Proof

Step	Hyp	Ref	Expression
1		ridl0.u	|- U = ( LIdeal ` ( oppR ` R ) )
2		ridl1.b	|- B = ( Base ` R )
3		eqid	|- ( oppR ` R ) = ( oppR ` R )
4	3	opprring	|- ( R e. Ring -> ( oppR ` R ) e. Ring )
5	3 2	opprbas	|- B = ( Base ` ( oppR ` R ) )
6	1 5	lidl1	|- ( ( oppR ` R ) e. Ring -> B e. U )
7	4 6	syl	|- ( R e. Ring -> B e. U )