Axiom ax-addcl 8083

Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddcl 8039. Proofs should normally use addcl 8112 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 7985	. . . 4 class CC
3	1, 2	wcel 2200	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2200	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		caddc 7990	. . . 4 class +
8	1, 4, 7	co 5994	. . 3 class ( A + B )
9	8, 2	wcel 2200	. 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  8112