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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | ⊢ 〈 〈 + , · 〉 , abs 〉 = 〈 〈 + , · 〉 , abs 〉 | |
2 | 1 | cnnv | ⊢ 〈 〈 + , · 〉 , abs 〉 ∈ NrmCVec |
3 | 2 | elimel | ⊢ if ( 𝑈 ∈ NrmCVec , 𝑈 , 〈 〈 + , · 〉 , abs 〉 ) ∈ NrmCVec |