Axiom ax-mulcl 8093

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulcl 8049. Proofs should normally use mulcl 8122 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 7993	. . . 4 class CC
3	1, 2	wcel 2200	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2200	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 8000	. . . 4 class x.
8	1, 4, 7	co 6000	. . 3 class ( A x. B )
9	8, 2	wcel 2200	. 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  8122