Axiom ax-mulrcl 9999

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom 7 of 22 for real and complex numbers, justified by theorem axmulrcl 9975. Proofs should normally use remulcl 10021 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 9935	. . . 4 class RR
3	1, 2	wcel 1990	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 1990	. . 3 wff B e. RR
6	3, 5	wa 384	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 9941	. . . 4 class x.
8	1, 4, 7	co 6650	. . 3 class ( A x. B )
9	8, 2	wcel 1990	. 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  10021