Metamath Proof Explorer


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 CPreHil OLD U + × abs CPreHil OLD

Proof

Step Hyp Ref Expression
1 eqid + × abs = + × abs
2 1 cncph + × abs CPreHil OLD
3 2 elimel if U CPreHil OLD U + × abs CPreHil OLD