Axiom ax-mulcl 7643

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 7601. Proofs should normally use mulcl 7671 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 7545	. . . 4 class CC
3	1, 2	wcel 1463	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1463	. . 3 wff B e. CC
6	3, 5	wa 103	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7552	. . . 4 class x.
8	1, 4, 7	co 5728	. . 3 class ( A x. B )
9	8, 2	wcel 1463	. 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  7671