Axiom ax-mulcl 9998

Description: Closure law for multiplication of complex numbers. Axiom 6 of 22 for real and complex numbers, justified by theorem axmulcl 9974. Proofs should normally use mulcl 10020 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 9934	. . . 4 class CC
3	1, 2	wcel 1990	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1990	. . 3 wff B e. CC
6	3, 5	wa 384	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 9941	. . . 4 class x.
8	1, 4, 7	co 6650	. . 3 class ( A x. B )
9	8, 2	wcel 1990	. 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  10020