Theorem mvrladdi

Description: Move the left term in a sum on the RHS to the LHS. (Contributed by David A. Wheeler, 11-Oct-2018)

	Ref	Expression
Hypotheses	mvrraddi.1	$$⊢B\in ℂ$$
	mvrraddi.2	$$⊢C\in ℂ$$
	mvrraddi.3	$$⊢A=B+C$$
Assertion	mvrladdi	$$⊢A-B=C$$

Proof

Step	Hyp	Ref	Expression
1		mvrraddi.1	$$⊢B\in ℂ$$
2		mvrraddi.2	$$⊢C\in ℂ$$
3		mvrraddi.3	$$⊢A=B+C$$
4	1 2 3	comraddi	$$⊢A=C+B$$
5	4	oveq1i	$$⊢A-B=C+B-B$$
6	2 1	pncan3oi	$$⊢C+B-B=C$$
7	5 6	eqtri	$$⊢A-B=C$$