Axiom ax-mulrcl 7712

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 7668. Proofs should normally use remulcl 7741 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 7612	. . . 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 7618	. . . 4 class x.
8	1, 4, 7	co 5767	. . 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  7741