Theorem hicl

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

	Ref	Expression
Assertion	hicl	⊢ ( ( 𝐴 ∈ ℋ ∧ 𝐵 ∈ ℋ ) → ( 𝐴 ·ih 𝐵 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		ax-hfi	⊢ ·ih : ( ℋ × ℋ ) ⟶ ℂ
2	1	fovcl	⊢ ( ( 𝐴 ∈ ℋ ∧ 𝐵 ∈ ℋ ) → ( 𝐴 ·ih 𝐵 ) ∈ ℂ )