Theorem add42i

Description: Rearrangement of 4 terms in a sum. (Contributed by NM, 22-Aug-1999) (Proof shortened by OpenAI, 25-Mar-2020)

	Ref	Expression
Hypotheses	add.1	$$⊢A\in ℂ$$
	add.2	$$⊢B\in ℂ$$
	add.3	$$⊢C\in ℂ$$
	add4.4	$$⊢D\in ℂ$$
Assertion	add42i	$$⊢A+B+C+D=A+C+D+B$$

Proof

Step	Hyp	Ref	Expression
1		add.1	$$⊢A\in ℂ$$
2		add.2	$$⊢B\in ℂ$$
3		add.3	$$⊢C\in ℂ$$
4		add4.4	$$⊢D\in ℂ$$
5		add42	$$⊢\left(\left(A\in ℂ\wedge B\in ℂ\right)\wedge \left(C\in ℂ\wedge D\in ℂ\right)\right)\to A+B+C+D=A+C+D+B$$
6	1 2 3 4 5	mp4an	$$⊢A+B+C+D=A+C+D+B$$