Theorem axmulcl

Description: Closure law for multiplication of complex numbers. Axiom 6 of 22 for real and complex numbers, derived from ZF set theory. This construction-dependent theorem should not be referenced directly, nor should the proven axiom ax-mulcl be used later. Instead, in most cases use mulcl . (Contributed by NM, 10-Aug-1995) (New usage is discouraged.)

	Ref	Expression
Assertion	axmulcl	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to AB\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		axmulf	$$⊢\times :ℂ\times ℂ⟶ℂ$$
2	1	fovcl	$$⊢\left(A\in ℂ\wedge B\in ℂ\right)\to AB\in ℂ$$