Axiom ax-mulrcl 8279

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 8235. Proofs should normally use remulcl 8308 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 8179	. . . 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 8185	. . . 4 class x.
8	1, 4, 7	co 6085	. . 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  8308