Theorem hicl

Description: Closure of inner product. (Contributed by NM, 17-Nov-2007) (New usage is discouraged.)

	Ref	Expression
Assertion	hicl	$$⊢\left(A\in \mathscr{H}\wedge B\in \mathscr{H}\right)\to A{\cdot }_{\mathrm{ih}}B\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		ax-hfi	$$⊢{\cdot }_{\mathrm{ih}}:\mathscr{H}\times \mathscr{H}⟶ℂ$$
2	1	fovcl	$$⊢\left(A\in \mathscr{H}\wedge B\in \mathscr{H}\right)\to A{\cdot }_{\mathrm{ih}}B\in ℂ$$