Axiom ax-mulrcl 7910

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 7866. Proofs should normally use remulcl 7939 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 7810	. . . 4 class RR
3	1, 2	wcel 2148	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2148	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 7816	. . . 4 class x.
8	1, 4, 7	co 5875	. . 3 class ( A x. B )
9	8, 2	wcel 2148	. 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  7939