Theorem mvrladdi

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

	Ref	Expression
Hypotheses	mvrraddi.1	|- B e. CC
	mvrraddi.2	|- C e. CC
	mvrraddi.3	|- A = ( B + C )
Assertion	mvrladdi	|- ( A - B ) = C

Proof

Step	Hyp	Ref	Expression
1		mvrraddi.1	|- B e. CC
2		mvrraddi.2	|- C e. CC
3		mvrraddi.3	|- A = ( B + C )
4	1 2 3	comraddi	|- A = ( C + B )
5	4	oveq1i	|- ( A - B ) = ( ( C + B ) - B )
6	2 1	pncan3oi	|- ( ( C + B ) - B ) = C
7	5 6	eqtri	|- ( A - B ) = C