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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 6737 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
2 | dffn3 6749 | . 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 5690 Fn wfn 6558 ⟶wf 6559 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ss 3980 df-f 6567 |
This theorem is referenced by: fo2ndf 8145 mapsnd 8925 itg1val2 25733 aks6d1c6lem3 42154 volicoff 45951 f1cof1b 47027 f1ocof1ob 47031 fundcmpsurbijinjpreimafv 47332 |
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