Theorem comraddd

Description: Commute RHS addition, in deduction form. (Contributed by David A. Wheeler, 11-Oct-2018)

	Ref	Expression
Hypotheses	comraddd.1	⊢ ( 𝜑 → 𝐵 ∈ ℂ )
	comraddd.2	⊢ ( 𝜑 → 𝐶 ∈ ℂ )
	comraddd.3	⊢ ( 𝜑 → 𝐴 = ( 𝐵 + 𝐶 ) )
Assertion	comraddd	⊢ ( 𝜑 → 𝐴 = ( 𝐶 + 𝐵 ) )

Proof

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