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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 6508 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
2 | dffn3 6519 | . 2 ⊢ (𝐹 Fn 𝐴 ↔ 𝐹:𝐴⟶ran 𝐹) | |
3 | 1, 2 | sylib 220 | 1 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹:𝐴⟶ran 𝐹) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ran crn 5550 Fn wfn 6344 ⟶wf 6345 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-in 3942 df-ss 3951 df-f 6353 |
This theorem is referenced by: fo2ndf 7811 mapsnd 8444 itg1val2 24279 selvval2lem4 39129 volicoff 42274 fundcmpsurbijinjpreimafv 43561 |
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