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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 5958 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
2 | dffn3 5967 | . 2 ⊢ (𝐹 Fn 𝐴 ↔ 𝐹:𝐴⟶ran 𝐹) | |
3 | 1, 2 | sylib 207 | 1 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹:𝐴⟶ran 𝐹) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ran crn 5039 Fn wfn 5799 ⟶wf 5800 |
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-in 3547 df-ss 3554 df-f 5808 |
This theorem is referenced by: volicoff 38888 frgrncvvdeqlemB 41477 |
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