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| Mirrors > Home > MPE Home > Th. List > ffrn | Structured version Visualization version GIF version | ||
| Description: A function maps to its range. (Contributed by Glauco Siliprandi, 3-Mar-2021.) |
| Ref | Expression |
|---|---|
| ffrn | ⊢ (𝐹:𝐴⟶𝐵 → 𝐹:𝐴⟶ran 𝐹) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ffn 6736 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
| 2 | dffn3 6748 | . 2 ⊢ (𝐹 Fn 𝐴 ↔ 𝐹:𝐴⟶ran 𝐹) | |
| 3 | 1, 2 | sylib 218 | 1 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹:𝐴⟶ran 𝐹) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ran crn 5686 Fn wfn 6556 ⟶wf 6557 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ss 3968 df-f 6565 |
| This theorem is referenced by: fo2ndf 8146 mapsnd 8926 itg1val2 25719 aks6d1c6lem3 42173 volicoff 46010 f1cof1b 47089 f1ocof1ob 47093 fundcmpsurbijinjpreimafv 47394 |
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