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Theorem funpartss 33302
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 Funpart𝐹𝐹

Proof of Theorem funpartss
StepHypRef Expression
1 df-funpart 33232 . 2 Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
2 resss 5871 . 2 (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))) ⊆ 𝐹
31, 2eqsstri 3998 1 Funpart𝐹𝐹
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3492  cin 3932  wss 3933   × cxp 5546  dom cdm 5548  cres 5550  ccom 5552  Singletoncsingle 33196   Singletons csingles 33197  Imagecimage 33198  Funpartcfunpart 33207
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-in 3940  df-ss 3949  df-res 5560  df-funpart 33232
This theorem is referenced by: (None)
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