Theorem mvlladdcd

Description: Rotate the variables right in an equation with addition on the left, converting it into a subtraction. Version of mvlladdd with a commuted consequent, and of mvrladdd with a commuted hypothesis. (Contributed by SN, 21-Aug-2024)

	Ref	Expression
Hypotheses	mvlraddd.1	$$⊢\phi \to A\in ℂ$$
	mvlraddd.2	$$⊢\phi \to B\in ℂ$$
	mvlraddd.3	$$⊢\phi \to A+B=C$$
Assertion	mvlladdcd	$$⊢\phi \to C-A=B$$

Proof

Step	Hyp	Ref	Expression
1		mvlraddd.1	$$⊢\phi \to A\in ℂ$$
2		mvlraddd.2	$$⊢\phi \to B\in ℂ$$
3		mvlraddd.3	$$⊢\phi \to A+B=C$$
4	1 2 3	mvlladdd	$$⊢\phi \to B=C-A$$
5	4	eqcomd	$$⊢\phi \to C-A=B$$