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	|- ( ph -> A e. CC )
	mvlraddd.2	|- ( ph -> B e. CC )
	mvlraddd.3	|- ( ph -> ( A + B ) = C )
Assertion	mvlladdd	|- ( ph -> B = ( C - A ) )

Proof

Step	Hyp	Ref	Expression
1		mvlraddd.1	|- ( ph -> A e. CC )
2		mvlraddd.2	|- ( ph -> B e. CC )
3		mvlraddd.3	|- ( ph -> ( A + B ) = C )
4	2 1	pncand	|- ( ph -> ( ( B + A ) - A ) = B )
5	1 2	addcomd	|- ( ph -> ( A + B ) = ( B + A ) )
6	5 3	eqtr3d	|- ( ph -> ( B + A ) = C )
7	6	oveq1d	|- ( ph -> ( ( B + A ) - A ) = ( C - A ) )
8	4 7	eqtr3d	|- ( ph -> B = ( C - A ) )