Axiom ax-mulcl 8005

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulcl 7961. Proofs should normally use mulcl 8034 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 7905	. . . 4 class CC
3	1, 2	wcel 2175	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2175	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7912	. . . 4 class x.
8	1, 4, 7	co 5934	. . 3 class ( A x. B )
9	8, 2	wcel 2175	. 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  8034