Theorem mplringd

Description: The polynomial ring is a ring. (Contributed by SN, 7-Feb-2025)

	Ref	Expression
Hypotheses	mplringd.p	|- P = ( I mPoly R )
	mplringd.i	|- ( ph -> I e. V )
	mplringd.r	|- ( ph -> R e. Ring )
Assertion	mplringd	|- ( ph -> P e. Ring )

Proof

Step	Hyp	Ref	Expression
1		mplringd.p	|- P = ( I mPoly R )
2		mplringd.i	|- ( ph -> I e. V )
3		mplringd.r	|- ( ph -> R e. Ring )
4	1	mplring	|- ( ( I e. V /\ R e. Ring ) -> P e. Ring )
5	2 3 4	syl2anc	|- ( ph -> P e. Ring )