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Theorem funpartss 24554
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 24486 . 2  |- Funpart F  =  ( F  |`  dom  (
(Image F  o. Singleton )  i^i  ( _V  X.  Singletons ) ) )
2 resss 4995 . 2  |-  ( F  |`  dom  ( (Image F  o. Singleton )  i^i  ( _V 
X.  Singletons ) ) ) 
C_  F
31, 2eqsstri 3221 1  |- Funpart F  C_  F
Colors of variables: wff set class
Syntax hints:   _Vcvv 2801    i^i cin 3164    C_ wss 3165    X. cxp 4703   dom cdm 4705    |` cres 4707    o. ccom 4709  Singletoncsingle 24452   Singletonscsingles 24453  Imagecimage 24454  Funpartcfunpart 24463
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179  df-res 4717  df-funpart 24486
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