Axiom ax-mulrcl 8284

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 8240. Proofs should normally use remulcl 8313 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 8184	. . . 4 class RR
3	1, 2	wcel 2209	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2209	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 8190	. . . 4 class x.
8	1, 4, 7	co 6088	. . 3 class ( A x. B )
9	8, 2	wcel 2209	. 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 used by:  remulcl  8313