Axiom ax-mulrcl 8054

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 8010. Proofs should normally use remulcl 8083 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 7954	. . . 4 class RR
3	1, 2	wcel 2177	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2177	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 7960	. . . 4 class x.
8	1, 4, 7	co 5962	. . 3 class ( A x. B )
9	8, 2	wcel 2177	. 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  8083