Theorem subnegi

Description: Relationship between subtraction and negative. (Contributed by NM, 1-Dec-2005)

	Ref	Expression
Hypotheses	negidi.1	$$⊢A\in ℂ$$
	pncan3i.2	$$⊢B\in ℂ$$
Assertion	subnegi	$$⊢A-\left(-B\right)=A+B$$

Proof

Step	Hyp	Ref	Expression
1		negidi.1	$$⊢A\in ℂ$$
2		pncan3i.2	$$⊢B\in ℂ$$
3		subneg	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to A-\left(-B\right)=A+B$$
4	1 2 3	mp2an	$$⊢A-\left(-B\right)=A+B$$