Axiom ax-mulcl 8241

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulcl 8197. Proofs should normally use mulcl 8270 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 8141	. . . 4 class CC
3	1, 2	wcel 2205	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2205	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 8148	. . . 4 class x.
8	1, 4, 7	co 6058	. . 3 class ( A x. B )
9	8, 2	wcel 2205	. 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  8270