Theorem add32r

Description: Commutative/associative law that swaps the last two terms in a triple sum, rearranging the parentheses. (Contributed by Paul Chapman, 18-May-2007)

	Ref	Expression
Assertion	add32r	$$⊢\left(A\in ℂ\wedge B\in ℂ\wedge C\in ℂ\right)\to A+B+C=A+C+B$$

Proof

Step	Hyp	Ref	Expression
1		addass	$$⊢\left(A\in ℂ\wedge B\in ℂ\wedge C\in ℂ\right)\to A+B+C=A+B+C$$
2		add32	$$⊢\left(A\in ℂ\wedge B\in ℂ\wedge C\in ℂ\right)\to A+B+C=A+C+B$$
3	1 2	eqtr3d	$$⊢\left(A\in ℂ\wedge B\in ℂ\wedge C\in ℂ\right)\to A+B+C=A+C+B$$