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Mathbox for Scott Fenton |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > funpartss | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
funpartss | ⊢ Funpart𝐹 ⊆ 𝐹 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-funpart 35855 | . 2 ⊢ Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))) | |
2 | resss 6021 | . 2 ⊢ (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))) ⊆ 𝐹 | |
3 | 1, 2 | eqsstri 4029 | 1 ⊢ Funpart𝐹 ⊆ 𝐹 |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3477 ∩ cin 3961 ⊆ wss 3962 × cxp 5686 dom cdm 5688 ↾ cres 5690 ∘ ccom 5692 Singletoncsingle 35819 Singletons csingles 35820 Imagecimage 35821 Funpartcfunpart 35830 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1539 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-v 3479 df-in 3969 df-ss 3979 df-res 5700 df-funpart 35855 |
This theorem is referenced by: (None) |
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