Axiom ax-mulrcl 7978

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 7934. Proofs should normally use remulcl 8007 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)

Assertion

Ref	Expression
ax-mulrcl	|- ( ( A e. RR /\ B e. RR ) -> ( A x. B ) e. RR )

Detailed syntax breakdown of Axiom ax-mulrcl

Step	Hyp	Ref	Expression
1		cA	. . . 4 class A
2		cr 7878	. . . 4 class RR
3	1, 2	wcel 2167	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2167	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 7884	. . . 4 class x.
8	1, 4, 7	co 5922	. . 3 class ( A x. B )
9	8, 2	wcel 2167	. 2 wff ( A x. B ) e. RR
10	6, 9	wi 4	1 wff ( ( A e. RR /\ B e. RR ) -> ( A x. B ) e. RR )

This axiom is referenced by:  remulcl  8007