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Theorem funpartss 34916
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 34846 . 2 Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
2 resss 6007 . 2 (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))) ⊆ 𝐹
31, 2eqsstri 4017 1 Funpart𝐹𝐹
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3475  cin 3948  wss 3949   × cxp 5675  dom cdm 5677  cres 5679  ccom 5681  Singletoncsingle 34810   Singletons csingles 34811  Imagecimage 34812  Funpartcfunpart 34821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966  df-res 5689  df-funpart 34846
This theorem is referenced by: (None)
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