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

Metamath Proof Explorer

Theorem vcex

Description: The components of a complex vector space are sets. (Contributed by NM, 31-May-2008) (New usage is discouraged.)

Ref Expression
Assertion vcex ⊢ G S ∈ CVec OLD → G ∈ V ∧ S ∈ V

Proof

Step Hyp Ref Expression
1 df-br ⊢ G CVec OLD S ↔ G S ∈ CVec OLD
2 vcrel ⊢ Rel ⁡ CVec OLD
3 2 brrelex12i ⊢ G CVec OLD S → G ∈ V ∧ S ∈ V
4 1 3 sylbir ⊢ G S ∈ CVec OLD → G ∈ V ∧ S ∈ V