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Mirrors > Home > ILE Home > Th. List > f1rel | GIF version |
Description: A one-to-one onto mapping is a relation. (Contributed by NM, 8-Mar-2014.) |
Ref | Expression |
---|---|
f1rel | ⊢ (𝐹:𝐴–1-1→𝐵 → Rel 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1fn 5093 | . 2 ⊢ (𝐹:𝐴–1-1→𝐵 → 𝐹 Fn 𝐴) | |
2 | fnrel 4997 | . 2 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝐹:𝐴–1-1→𝐵 → Rel 𝐹) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Rel wrel 4350 Fn wfn 4897 –1-1→wf1 4899 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 |
This theorem depends on definitions: df-bi 110 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 |
This theorem is referenced by: (None) |
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