Axiom ax-addcl 7709

Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by theorem axaddcl 7665. Proofs should normally use addcl 7738 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 7611	. . . 4 class CC
3	1, 2	wcel 1480	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1480	. . 3 wff B e. CC
6	3, 5	wa 103	. 2 wff ( A e. CC /\ B e. CC )
7		caddc 7616	. . . 4 class +
8	1, 4, 7	co 5767	. . 3 class ( A + B )
9	8, 2	wcel 1480	. 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  7738