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Metamath Proof Explorer

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