Theorem subeq0i

Description: If the difference between two numbers is zero, they are equal. (Contributed by NM, 8-May-1999)

	Ref	Expression
Hypotheses	negidi.1	$$⊢A\in ℂ$$
	pncan3i.2	$$⊢B\in ℂ$$
Assertion	subeq0i	$$⊢A-B=0\leftrightarrow A=B$$

Proof

Step	Hyp	Ref	Expression
1		negidi.1	$$⊢A\in ℂ$$
2		pncan3i.2	$$⊢B\in ℂ$$
3		subeq0	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to \left(A-B=0\leftrightarrow A=B\right)$$
4	1 2 3	mp2an	$$⊢A-B=0\leftrightarrow A=B$$