Axiom ax-mulcl 7977

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulcl 7933. Proofs should normally use mulcl 8006 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 7877	. . . 4 class CC
3	1, 2	wcel 2167	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2167	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7884	. . . 4 class x.
8	1, 4, 7	co 5922	. . 3 class ( A x. B )
9	8, 2	wcel 2167	. 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  8006