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