Theorem mvlladdi

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

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

Proof

Step	Hyp	Ref	Expression
1		mvlladdi.1	$$⊢A\in ℂ$$
2		mvlladdi.2	$$⊢B\in ℂ$$
3		mvlladdi.3	$$⊢A+B=C$$
4	2 1	pncan3oi	$$⊢B+A-A=B$$
5	1 2 3	addcomli	$$⊢B+A=C$$
6	5	oveq1i	$$⊢B+A-A=C-A$$
7	4 6	eqtr3i	$$⊢B=C-A$$