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Mirrors > Home > ILE Home > Th. List > f1fun | GIF version |
Description: A one-to-one mapping is a function. (Contributed by NM, 8-Mar-2014.) |
Ref | Expression |
---|---|
f1fun | ⊢ (𝐹:𝐴–1-1→𝐵 → Fun 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1fn 5113 | . 2 ⊢ (𝐹:𝐴–1-1→𝐵 → 𝐹 Fn 𝐴) | |
2 | fnfun 5016 | . 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝐹:𝐴–1-1→𝐵 → Fun 𝐹) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Fun wfun 4916 Fn wfn 4917 –1-1→wf1 4919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 |
This theorem depends on definitions: df-bi 115 df-fn 4925 df-f 4926 df-f1 4927 |
This theorem is referenced by: f1cocnv2 5174 f1o2ndf1 5869 f1dmvrnfibi 6393 |
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