Axiom ax-mulrcl 7843

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 7799. Proofs should normally use remulcl 7872 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 7743	. . . 4 class RR
3	1, 2	wcel 2135	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2135	. . 3 wff B e. RR
6	3, 5	wa 103	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 7749	. . . 4 class x.
8	1, 4, 7	co 5836	. . 3 class ( A x. B )
9	8, 2	wcel 2135	. 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  7872