Theorem hicli

Description: Closure inference for inner product. (Contributed by NM, 1-Aug-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	hicl.1	⊢ 𝐴 ∈ ℋ
	hicl.2	⊢ 𝐵 ∈ ℋ
Assertion	hicli	⊢ ( 𝐴 ·ih 𝐵 ) ∈ ℂ

Proof

Step	Hyp	Ref	Expression
1		hicl.1	⊢ 𝐴 ∈ ℋ
2		hicl.2	⊢ 𝐵 ∈ ℋ
3		hicl	⊢ ( ( 𝐴 ∈ ℋ ∧ 𝐵 ∈ ℋ ) → ( 𝐴 ·ih 𝐵 ) ∈ ℂ )
4	1 2 3	mp2an	⊢ ( 𝐴 ·ih 𝐵 ) ∈ ℂ