Theorem addcli

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

	Ref	Expression
Hypotheses	axi.1	|- A e. CC
	axi.2	|- B e. CC
Assertion	addcli	|- ( A + B ) e. CC

Proof

Step	Hyp	Ref	Expression
1		axi.1	|- A e. CC
2		axi.2	|- B e. CC
3		addcl	|- ( ( A e. CC /\ B e. CC ) -> ( A + B ) e. CC )
4	1 2 3	mp2an	|- ( A + B ) e. CC