Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
||
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 31150 | . 2 ⊢ Funpart𝐹 = (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))) | |
2 | resss 5342 | . 2 ⊢ (𝐹 ↾ dom ((Image𝐹 ∘ Singleton) ∩ (V × Singletons ))) ⊆ 𝐹 | |
3 | 1, 2 | eqsstri 3598 | 1 ⊢ Funpart𝐹 ⊆ 𝐹 |
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) |
Copyright terms: Public domain | W3C validator |