Theorem mvrraddi

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

	Ref	Expression
Hypotheses	mvrraddi.1	⊢ 𝐵 ∈ ℂ
	mvrraddi.2	⊢ 𝐶 ∈ ℂ
	mvrraddi.3	⊢ 𝐴 = ( 𝐵 + 𝐶 )
Assertion	mvrraddi	⊢ ( 𝐴 − 𝐶 ) = 𝐵

Proof

Step	Hyp	Ref	Expression
1		mvrraddi.1	⊢ 𝐵 ∈ ℂ
2		mvrraddi.2	⊢ 𝐶 ∈ ℂ
3		mvrraddi.3	⊢ 𝐴 = ( 𝐵 + 𝐶 )
4	3	oveq1i	⊢ ( 𝐴 − 𝐶 ) = ( ( 𝐵 + 𝐶 ) − 𝐶 )
5	1 2	pncan3oi	⊢ ( ( 𝐵 + 𝐶 ) − 𝐶 ) = 𝐵
6	4 5	eqtri	⊢ ( 𝐴 − 𝐶 ) = 𝐵