Axiom ax-mulcl 7711

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 7667. Proofs should normally use mulcl 7740 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 7611	. . . 4 class CC
3	1, 2	wcel 1480	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1480	. . 3 wff B e. CC
6	3, 5	wa 103	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7618	. . . 4 class x.
8	1, 4, 7	co 5767	. . 3 class ( A x. B )
9	8, 2	wcel 1480	. 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  7740