This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem hvmulcli

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

Ref Expression
Hypotheses hvmulcl.1 ⊢ A ∈ ℂ
hvmulcl.2 ⊢ B ∈ ℋ
Assertion hvmulcli ⊢ A ⋅ ℎ B ∈ ℋ

Proof

Step Hyp Ref Expression
1 hvmulcl.1 ⊢ A ∈ ℂ
2 hvmulcl.2 ⊢ B ∈ ℋ
3 hvmulcl ⊢ A ∈ ℂ ∧ B ∈ ℋ → A ⋅ ℎ B ∈ ℋ
4 1 2 3 mp2an ⊢ A ⋅ ℎ B ∈ ℋ