Axiom ax-mulrcl 8023

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 7979. Proofs should normally use remulcl 8052 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 7923	. . . 4 class RR
3	1, 2	wcel 2175	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2175	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 7929	. . . 4 class x.
8	1, 4, 7	co 5943	. . 3 class ( A x. B )
9	8, 2	wcel 2175	. 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  8052