Metamath Proof Explorer


Theorem elimnvu

Description: Hypothesis elimination lemma for normed complex vector spaces to assist weak deduction theorem. (Contributed by NM, 16-May-2007) (New usage is discouraged.)

Ref Expression
Assertion elimnvu if ( 𝑈 ∈ NrmCVec , 𝑈 , ⟨ ⟨ + , · ⟩ , abs ⟩ ) ∈ NrmCVec

Proof

Step Hyp Ref Expression
1 eqid ⟨ ⟨ + , · ⟩ , abs ⟩ = ⟨ ⟨ + , · ⟩ , abs ⟩
2 1 cnnv ⟨ ⟨ + , · ⟩ , abs ⟩ ∈ NrmCVec
3 2 elimel if ( 𝑈 ∈ NrmCVec , 𝑈 , ⟨ ⟨ + , · ⟩ , abs ⟩ ) ∈ NrmCVec