Axiom ax-mulcl 6982

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 6942. Proofs should normally use mulcl 7008 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)

Assertion

Ref	Expression
ax-mulcl	|- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) e. CC )

Detailed syntax breakdown of Axiom ax-mulcl

Step	Hyp	Ref	Expression
1		cA	. . . 4 class A
2		cc 6887	. . . 4 class CC
3	1, 2	wcel 1393	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1393	. . 3 wff B e. CC
6	3, 5	wa 97	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 6894	. . . 4 class x.
8	1, 4, 7	co 5512	. . 3 class ( A x. B )
9	8, 2	wcel 1393	. 2 wff ( A x. B ) e. CC
10	6, 9	wi 4	1 wff ( ( A e. CC /\ B e. CC ) -> ( A x. B ) e. CC )

This axiom is referenced by:  mulcl  7008