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	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
	mvlraddd.2	⊢ ( 𝜑 → 𝐵 ∈ ℂ )
	mvlraddd.3	⊢ ( 𝜑 → ( 𝐴 + 𝐵 ) = 𝐶 )
Assertion	mvlraddd	⊢ ( 𝜑 → 𝐴 = ( 𝐶 − 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		mvlraddd.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		mvlraddd.2	⊢ ( 𝜑 → 𝐵 ∈ ℂ )
3		mvlraddd.3	⊢ ( 𝜑 → ( 𝐴 + 𝐵 ) = 𝐶 )
4	1 2	pncand	⊢ ( 𝜑 → ( ( 𝐴 + 𝐵 ) − 𝐵 ) = 𝐴 )
5	3	oveq1d	⊢ ( 𝜑 → ( ( 𝐴 + 𝐵 ) − 𝐵 ) = ( 𝐶 − 𝐵 ) )
6	4 5	eqtr3d	⊢ ( 𝜑 → 𝐴 = ( 𝐶 − 𝐵 ) )