Theorem rlmbas

Description: Base set of the ring module. (Contributed by Stefan O'Rear, 31-Mar-2015)

	Ref	Expression
Assertion	rlmbas	|- ( Base ` R ) = ( Base ` ( ringLMod ` R ) )

Proof

Step	Hyp	Ref	Expression
1		rlmval	|- ( ringLMod ` R ) = ( ( subringAlg ` R ) ` ( Base ` R ) )
2	1	a1i	|- ( T. -> ( ringLMod ` R ) = ( ( subringAlg ` R ) ` ( Base ` R ) ) )
3		ssidd	|- ( T. -> ( Base ` R ) C_ ( Base ` R ) )
4	2 3	srabase	|- ( T. -> ( Base ` R ) = ( Base ` ( ringLMod ` R ) ) )
5	4	mptru	|- ( Base ` R ) = ( Base ` ( ringLMod ` R ) )