Axiom ax-mulcl 7039

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 6999. Proofs should normally use mulcl 7065 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 6944	. . . 4 class CC
3	1, 2	wcel 1409	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1409	. . 3 wff B e. CC
6	3, 5	wa 101	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 6951	. . . 4 class x.
8	1, 4, 7	co 5539	. . 3 class ( A x. B )
9	8, 2	wcel 1409	. 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  7065