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Theorem funpartss 31221
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 31150 . 2 Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
2 resss 5342 . 2 (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))) ⊆ 𝐹
31, 2eqsstri 3598 1 Funpart𝐹𝐹
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3173  cin 3539  wss 3540   × cxp 5036  dom cdm 5038  cres 5040  ccom 5042  Singletoncsingle 31114   Singletons csingles 31115  Imagecimage 31116  Funpartcfunpart 31125
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-in 3547  df-ss 3554  df-res 5050  df-funpart 31150
This theorem is referenced by: (None)
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