Axiom ax-mulrcl 8109

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 8065. Proofs should normally use remulcl 8138 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 8009	. . . 4 class RR
3	1, 2	wcel 2200	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2200	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 8015	. . . 4 class x.
8	1, 4, 7	co 6007	. . 3 class ( A x. B )
9	8, 2	wcel 2200	. 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  8138