Metamath Proof Explorer

Theorem hlcph

Description: Every subcomplex Hilbert space is a subcomplex pre-Hilbert space. (Contributed by Mario Carneiro, 15-Oct-2015)

Ref Expression
Assertion hlcph 
|- ( W e. CHil -> W e. CPreHil )

Proof

Step Hyp Ref Expression
1 ishl 
 |-  ( W e. CHil <-> ( W e. Ban /\ W e. CPreHil ) )
2 1 simprbi 
 |-  ( W e. CHil -> W e. CPreHil )