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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 5422 | . 2 ⊢ (𝐹:𝐴–1-1→𝐵 → 𝐹 Fn 𝐴) | |
2 | fnfun 5312 | . 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 5209 Fn wfn 5210 –1-1→wf1 5212 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 |
This theorem depends on definitions: df-bi 117 df-fn 5218 df-f 5219 df-f1 5220 |
This theorem is referenced by: f1cocnv2 5488 f1o2ndf1 6226 f1dmvrnfibi 6940 djuinj 7102 |
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