Axiom ax-mulrcl 8024

Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by Theorem axmulrcl 7980. Proofs should normally use remulcl 8053 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 7924	. . . 4 class RR
3	1, 2	wcel 2176	. . 3 wff A e. RR
4		cB	. . . 4 class B
5	4, 2	wcel 2176	. . 3 wff B e. RR
6	3, 5	wa 104	. 2 wff ( A e. RR /\ B e. RR )
7		cmul 7930	. . . 4 class x.
8	1, 4, 7	co 5944	. . 3 class ( A x. B )
9	8, 2	wcel 2176	. 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  8053