Theorem addsubi

Description: Law for subtraction and addition. (Contributed by NM, 6-Aug-2003)

	Ref	Expression
Hypotheses	negidi.1	$$⊢A\in ℂ$$
	pncan3i.2	$$⊢B\in ℂ$$
	subadd.3	$$⊢C\in ℂ$$
Assertion	addsubi	$$⊢A+B-C=A-C+B$$

Proof

Step	Hyp	Ref	Expression
1		negidi.1	$$⊢A\in ℂ$$
2		pncan3i.2	$$⊢B\in ℂ$$
3		subadd.3	$$⊢C\in ℂ$$
4		addsub	$$⊢\left(A\in ℂ\wedge B\in ℂ\wedge C\in ℂ\right)\to A+B-C=A-C+B$$
5	1 2 3 4	mp3an	$$⊢A+B-C=A-C+B$$