Theorem subcli

Description: Closure law for subtraction. (Contributed by NM, 26-Nov-1994) (Revised by Mario Carneiro, 21-Dec-2013)

	Ref	Expression
Hypotheses	negidi.1	$$⊢A\in ℂ$$
	pncan3i.2	$$⊢B\in ℂ$$
Assertion	subcli	$$⊢A-B\in ℂ$$

Proof

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