Axiom ax-addcl 7909

Description: Closure law for addition of complex numbers. Axiom for real and complex numbers, justified by Theorem axaddcl 7865. Proofs should normally use addcl 7938 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 7811	. . . 4 class CC
3	1, 2	wcel 2148	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2148	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		caddc 7816	. . . 4 class +
8	1, 4, 7	co 5877	. . 3 class ( A + B )
9	8, 2	wcel 2148	. 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  7938