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	$$⊢if\left(U\in \mathrm{NrmCVec},U,⟨⟨+,\times ⟩,\mathrm{abs}⟩\right)\in \mathrm{NrmCVec}$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢⟨⟨+,\times ⟩,\mathrm{abs}⟩=⟨⟨+,\times ⟩,\mathrm{abs}⟩$$
2	1	cnnv	$$⊢⟨⟨+,\times ⟩,\mathrm{abs}⟩\in \mathrm{NrmCVec}$$
3	2	elimel	$$⊢if\left(U\in \mathrm{NrmCVec},U,⟨⟨+,\times ⟩,\mathrm{abs}⟩\right)\in \mathrm{NrmCVec}$$