Axiom ax-mulrcl 7594

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 7554. Proofs should normally use remulcl 7620 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 7499	. . . 4 class RR
3	1, 2	wcel 1448	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 1448	. . 3 wff B e. RR
6	3, 5	wa 103	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 7505	. . . 4 class x.
8	1, 4, 7	co 5706	. . 3 class ( A x. B )
9	8, 2	wcel 1448	. 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  7620