Theorem mvrladdd

Description: Move the left 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	⊢ ( 𝜑 → 𝐵 ∈ ℂ )
	mvrraddd.2	⊢ ( 𝜑 → 𝐶 ∈ ℂ )
	mvrraddd.3	⊢ ( 𝜑 → 𝐴 = ( 𝐵 + 𝐶 ) )
Assertion	mvrladdd	⊢ ( 𝜑 → ( 𝐴 − 𝐵 ) = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		mvrraddd.1	⊢ ( 𝜑 → 𝐵 ∈ ℂ )
2		mvrraddd.2	⊢ ( 𝜑 → 𝐶 ∈ ℂ )
3		mvrraddd.3	⊢ ( 𝜑 → 𝐴 = ( 𝐵 + 𝐶 ) )
4	1 2 3	comraddd	⊢ ( 𝜑 → 𝐴 = ( 𝐶 + 𝐵 ) )
5	2 1 4	mvrraddd	⊢ ( 𝜑 → ( 𝐴 − 𝐵 ) = 𝐶 )