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Mirrors > Home > ILE Home > Th. List > f1orel | GIF version |
Description: A one-to-one onto mapping is a relation. (Contributed by NM, 13-Dec-2003.) |
Ref | Expression |
---|---|
f1orel | ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Rel 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1ofun 5337 | . 2 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Fun 𝐹) | |
2 | funrel 5110 | . 2 ⊢ (Fun 𝐹 → Rel 𝐹) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Rel 𝐹) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Rel wrel 4514 Fun wfun 5087 –1-1-onto→wf1o 5092 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 |
This theorem depends on definitions: df-bi 116 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-f1o 5100 |
This theorem is referenced by: f1ococnv1 5364 isores1 5683 ssenen 6713 dif1en 6741 |
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