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Theorem funpartss 25500
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.)
Assertion
Ref Expression
funpartss  |- Funpart F  C_  F

Proof of Theorem funpartss
StepHypRef Expression
1 df-funpart 25432 . 2  |- Funpart F  =  ( F  |`  dom  (
(Image F  o. Singleton )  i^i  ( _V  X.  Singletons ) ) )
2 resss 5103 . 2  |-  ( F  |`  dom  ( (Image F  o. Singleton )  i^i  ( _V 
X.  Singletons ) ) ) 
C_  F
31, 2eqsstri 3314 1  |- Funpart F  C_  F
Colors of variables: wff set class
Syntax hints:   _Vcvv 2892    i^i cin 3255    C_ wss 3256    X. cxp 4809   dom cdm 4811    |` cres 4813    o. ccom 4815  Singletoncsingle 25398   Singletonscsingles 25399  Imagecimage 25400  Funpartcfunpart 25409
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-v 2894  df-in 3263  df-ss 3270  df-res 4823  df-funpart 25432
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