Axiom ax-mulrcl 7719

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 7675. Proofs should normally use remulcl 7748 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 7619	. . . 4 class RR
3	1, 2	wcel 1480	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 1480	. . 3 wff B e. RR
6	3, 5	wa 103	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 7625	. . . 4 class x.
8	1, 4, 7	co 5774	. . 3 class ( A x. B )
9	8, 2	wcel 1480	. 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  7748