Theorem mvlraddd

Description: Move the right 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	mvlraddd	|- ( ph -> A = ( C - B ) )

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	1 2	pncand	|- ( ph -> ( ( A + B ) - B ) = A )
5	3	oveq1d	|- ( ph -> ( ( A + B ) - B ) = ( C - B ) )
6	4 5	eqtr3d	|- ( ph -> A = ( C - B ) )