Theorem addcli

Description: Closure law for addition. (Contributed by NM, 23-Nov-1994)

	Ref	Expression
Hypotheses	axi.1	$$⊢A\in ℂ$$
	axi.2	$$⊢B\in ℂ$$
Assertion	addcli	$$⊢A+B\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		axi.1	$$⊢A\in ℂ$$
2		axi.2	$$⊢B\in ℂ$$
3		addcl	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to A+B\in ℂ$$
4	1 2 3	mp2an	$$⊢A+B\in ℂ$$