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	$$⊢R={ℂ}_{\mathrm{fld}}{\upharpoonright }_{𝑠}S$$
Assertion	cnfldsrngmul	$$⊢S\in V\to \times ={\cdot }_R$$

Proof

Step	Hyp	Ref	Expression
1		cnfldsrngbas.r	$$⊢R={ℂ}_{\mathrm{fld}}{\upharpoonright }_{𝑠}S$$
2		cnfldmul	$$⊢\times ={\cdot }_{{ℂ}_{\mathrm{fld}}}$$
3	1 2	ressmulr	$$⊢S\in V\to \times ={\cdot }_R$$