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 e. CPreHilOLD , U , <. <. + , x. >. , abs >. ) e. CPreHilOLD

Proof

Step	Hyp	Ref	Expression
1		eqid	|- <. <. + , x. >. , abs >. = <. <. + , x. >. , abs >.
2	1	cncph	|- <. <. + , x. >. , abs >. e. CPreHilOLD
3	2	elimel	|- if ( U e. CPreHilOLD , U , <. <. + , x. >. , abs >. ) e. CPreHilOLD