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Theorem funpartss 33795
 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 33725 . 2 Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
2 resss 5848 . 2 (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))) ⊆ 𝐹
31, 2eqsstri 3926 1 Funpart𝐹𝐹
 Colors of variables: wff setvar class Syntax hints:  Vcvv 3409   ∩ cin 3857   ⊆ wss 3858   × cxp 5522  dom cdm 5524   ↾ cres 5526   ∘ ccom 5528  Singletoncsingle 33689   Singletons csingles 33690  Imagecimage 33691  Funpartcfunpart 33700 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-v 3411  df-in 3865  df-ss 3875  df-res 5536  df-funpart 33725 This theorem is referenced by: (None)
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