Metamath Proof Explorer


Definition df-ba

Description: Define the base set of a normed complex vector space. (Contributed by NM, 23-Apr-2007) (New usage is discouraged.)

Ref Expression
Assertion df-ba BaseSet = ( 𝑥 ∈ V ↦ ran ( +𝑣 ‘ 𝑥 ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cba ⊢ BaseSet
1 vx ⊢ 𝑥
2 cvv ⊢ V
3 cpv ⊢ +𝑣
4 1 cv ⊢ 𝑥
5 4 3 cfv ⊢ ( +𝑣 ‘ 𝑥 )
6 5 crn ⊢ ran ( +𝑣 ‘ 𝑥 )
7 1 2 6 cmpt ⊢ ( 𝑥 ∈ V ↦ ran ( +𝑣 ‘ 𝑥 ) )
8 0 7 wceq ⊢ BaseSet = ( 𝑥 ∈ V ↦ ran ( +𝑣 ‘ 𝑥 ) )