Axiom ax-mulcl 8043

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulcl 7999. Proofs should normally use mulcl 8072 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 7943	. . . 4 class CC
3	1, 2	wcel 2177	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2177	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7950	. . . 4 class x.
8	1, 4, 7	co 5957	. . 3 class ( A x. B )
9	8, 2	wcel 2177	. 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  8072