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Mirrors > Home > ILE Home > Th. List > frel | GIF version |
Description: A mapping is a relation. (Contributed by NM, 3-Aug-1994.) |
Ref | Expression |
---|---|
frel | ⊢ (𝐹:𝐴⟶𝐵 → Rel 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffn 5176 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
2 | fnrel 5127 | . 2 ⊢ (𝐹 Fn 𝐴 → Rel 𝐹) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝐹:𝐴⟶𝐵 → Rel 𝐹) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Rel wrel 4459 Fn wfn 5025 ⟶wf 5026 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 |
This theorem depends on definitions: df-bi 116 df-fun 5032 df-fn 5033 df-f 5034 |
This theorem is referenced by: fssxp 5193 fsn 5485 eluzel2 9087 |
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