Theorem cnfldsrngmul

Description: The ring multiplication operation of a subring of the field of complex numbers. (Contributed by AV, 31-Jan-2020)

	Ref	Expression
Hypothesis	cnfldsrngbas.r	|- R = ( CCfld |`s S )
Assertion	cnfldsrngmul	|- ( S e. V -> x. = ( .r ` R ) )

Proof

Step	Hyp	Ref	Expression
1		cnfldsrngbas.r	|- R = ( CCfld |`s S )
2		cnfldmul	|- x. = ( .r ` CCfld )
3	1 2	ressmulr	|- ( S e. V -> x. = ( .r ` R ) )