Axiom ax-mulrcl 7973

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 7929. Proofs should normally use remulcl 8002 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 7873	. . . 4 class RR
3	1, 2	wcel 2164	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2164	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 7879	. . . 4 class x.
8	1, 4, 7	co 5919	. . 3 class ( A x. B )
9	8, 2	wcel 2164	. 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  8002