Axiom ax-addcl 7975

Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddcl 7931. Proofs should normally use addcl 8004 instead, which asserts the same thing but follows our naming conventions for closures. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)

Assertion

Ref	Expression
ax-addcl	|- ( ( A e. CC /\ B e. CC ) -> ( A + B ) e. CC )

Detailed syntax breakdown of Axiom ax-addcl

Step	Hyp	Ref	Expression
1		cA	. . . 4 class A
2		cc 7877	. . . 4 class CC
3	1, 2	wcel 2167	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2167	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		caddc 7882	. . . 4 class +
8	1, 4, 7	co 5922	. . 3 class ( A + B )
9	8, 2	wcel 2167	. 2 wff ( A + B ) e. CC
10	6, 9	wi 4	1 wff ( ( A e. CC /\ B e. CC ) -> ( A + B ) e. CC )

This axiom is referenced by:  addcl  8004