Axiom ax-mulrcl 7075

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 7035. Proofs should normally use remulcl 7101 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 6980	. . . 4 class RR
3	1, 2	wcel 1433	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 1433	. . 3 wff B e. RR
6	3, 5	wa 102	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 6986	. . . 4 class x.
8	1, 4, 7	co 5532	. . 3 class ( A x. B )
9	8, 2	wcel 1433	. 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  7101