Axiom ax-mulcl 7074

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 7034. Proofs should normally use mulcl 7100 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 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		cmul 6986	. . . 4 class x.
8	1, 4, 7	co 5532	. . 3 class ( A x. B )
9	8, 2	wcel 1433	. 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  7100