Theorem mvrraddd

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

	Ref	Expression
Hypotheses	mvrraddd.1	|- ( ph -> B e. CC )
	mvrraddd.2	|- ( ph -> C e. CC )
	mvrraddd.3	|- ( ph -> A = ( B + C ) )
Assertion	mvrraddd	|- ( ph -> ( A - C ) = B )

Proof

Step	Hyp	Ref	Expression
1		mvrraddd.1	|- ( ph -> B e. CC )
2		mvrraddd.2	|- ( ph -> C e. CC )
3		mvrraddd.3	|- ( ph -> A = ( B + C ) )
4	3	oveq1d	|- ( ph -> ( A - C ) = ( ( B + C ) - C ) )
5	1 2	pncand	|- ( ph -> ( ( B + C ) - C ) = B )
6	4 5	eqtrd	|- ( ph -> ( A - C ) = B )