Axiom ax-addcl 7072

Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by theorem axaddcl 7032. Proofs should normally use addcl 7098 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 6979	. . . 4 class CC
3	1, 2	wcel 1433	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1433	. . 3 wff B e. CC
6	3, 5	wa 102	. 2 wff ( A e. CC /\ B e. CC )
7		caddc 6984	. . . 4 class +
8	1, 4, 7	co 5532	. . 3 class ( A + B )
9	8, 2	wcel 1433	. 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  7098