Axiom ax-mulcl 7908

Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulcl 7864. Proofs should normally use mulcl 7937 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 7808	. . . 4 class CC
3	1, 2	wcel 2148	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2148	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7815	. . . 4 class x.
8	1, 4, 7	co 5874	. . 3 class ( A x. B )
9	8, 2	wcel 2148	. 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  7937