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Theorem funpartss 31714
 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 31643 . 2 Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons )))
2 resss 5383 . 2 (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))) ⊆ 𝐹
31, 2eqsstri 3616 1 Funpart𝐹𝐹
 Colors of variables: wff setvar class Syntax hints:  Vcvv 3186   ∩ cin 3555   ⊆ wss 3556   × cxp 5074  dom cdm 5076   ↾ cres 5078   ∘ ccom 5080  Singletoncsingle 31607   Singletons csingles 31608  Imagecimage 31609  Funpartcfunpart 31618 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-in 3563  df-ss 3570  df-res 5088  df-funpart 31643 This theorem is referenced by: (None)
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