Metamath Proof Explorer

Theorem funpartss

Description: The functional part of F is a subset of F . (Contributed by Scott Fenton, 17-Apr-2014) (Revised by Mario Carneiro, 19-Apr-2014)

Ref Expression
Assertion funpartss 
|- Funpart F C_ F

Proof

Step Hyp Ref Expression
1 df-funpart 
 |-  Funpart F = ( F |` dom ( ( Image F o. Singleton ) i^i ( _V X. Singletons ) ) )
2 resss 
 |-  ( F |` dom ( ( Image F o. Singleton ) i^i ( _V X. Singletons ) ) ) C_ F
3 1 2 eqsstri 
 |-  Funpart F C_ F