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Theorem funpartss 24482
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 24415 . 2  |- Funpart F  =  ( F  |`  dom  (
(Image F  o. Singleton )  i^i  ( _V  X.  Singletons ) ) )
2 resss 4979 . 2  |-  ( F  |`  dom  ( (Image F  o. Singleton )  i^i  ( _V 
X.  Singletons ) ) ) 
C_  F
31, 2eqsstri 3208 1  |- Funpart F  C_  F
Colors of variables: wff set class
Syntax hints:   _Vcvv 2788    i^i cin 3151    C_ wss 3152    X. cxp 4687   dom cdm 4689    |` cres 4691    o. ccom 4693  Singletoncsingle 24381   Singletonscsingles 24382  Imagecimage 24383  Funpartcfunpart 24392
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-ss 3166  df-res 4701  df-funpart 24415
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