Axiom ax-mulcl 6781

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 6752. Proofs should normally use mulcl 6806 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 6709	. . . 4 class CC
3	1, 2	wcel 1390	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1390	. . 3 wff B e. CC
6	3, 5	wa 97	. 2 wff (A e. CC /\ B e. CC)
7		cmul 6716	. . . 4 class x.
8	1, 4, 7	co 5455	. . 3 class (A x. B)
9	8, 2	wcel 1390	. 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  6806