Axiom ax-mulcl 7206

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 7166. Proofs should normally use mulcl 7232 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 7111	. . . 4 class CC
3	1, 2	wcel 1434	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1434	. . 3 wff B e. CC
6	3, 5	wa 102	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7118	. . . 4 class x.
8	1, 4, 7	co 5564	. . 3 class ( A x. B )
9	8, 2	wcel 1434	. 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  7232