Theorem mvlladdd

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

	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	mvlladdd	$$⊢\phi \to B=C-A$$

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	2 1	pncand	$$⊢\phi \to B+A-A=B$$
5	1 2	addcomd	$$⊢\phi \to A+B=B+A$$
6	5 3	eqtr3d	$$⊢\phi \to B+A=C$$
7	6	oveq1d	$$⊢\phi \to B+A-A=C-A$$
8	4 7	eqtr3d	$$⊢\phi \to B=C-A$$