Theorem elimphu

Description: Hypothesis elimination lemma for complex inner product spaces to assist weak deduction theorem. (Contributed by NM, 6-May-2007) (New usage is discouraged.)

	Ref	Expression
Assertion	elimphu	⊢ if ( 𝑈 ∈ CPreHilOLD , 𝑈 , ⟨ ⟨ + , · ⟩ , abs ⟩ ) ∈ CPreHilOLD

Proof

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