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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 5362 | . 2 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Fun 𝐹) | |
2 | funrel 5135 | . 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 4539 Fun wfun 5112 –1-1-onto→wf1o 5117 |
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 5120 df-fn 5121 df-f 5122 df-f1 5123 df-f1o 5125 |
This theorem is referenced by: f1ococnv1 5389 isores1 5708 ssenen 6738 dif1en 6766 |
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