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 e. CC
	mvlladdi.2	|- B e. CC
	mvlladdi.3	|- ( A + B ) = C
Assertion	mvlladdi	|- B = ( C - A )

Proof

Step	Hyp	Ref	Expression
1		mvlladdi.1	|- A e. CC
2		mvlladdi.2	|- B e. CC
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 )