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

Metamath Proof Explorer

Theorem dvhopclN

Description: Closure of a DVecH vector expressed as ordered pair. (Contributed by NM, 20-Nov-2013) (New usage is discouraged.)

Ref Expression
Assertion dvhopclN ( ( 𝐹 ∈ 𝑇 ∧ 𝑈 ∈ 𝐸 ) → ⟨ 𝐹 , 𝑈 ⟩ ∈ ( 𝑇 × 𝐸 ) )

Proof

Step Hyp Ref Expression
1 opelxpi ⊢ ( ( 𝐹 ∈ 𝑇 ∧ 𝑈 ∈ 𝐸 ) → ⟨ 𝐹 , 𝑈 ⟩ ∈ ( 𝑇 × 𝐸 ) )