Axiom ax-mulrcl 8242

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 8198. Proofs should normally use remulcl 8271 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 8142	. . . 4 class RR
3	1, 2	wcel 2205	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2205	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 8148	. . . 4 class x.
8	1, 4, 7	co 6058	. . 3 class ( A x. B )
9	8, 2	wcel 2205	. 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  8271