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Mirrors > Home > ILE Home > Th. List > fdmi | GIF version |
Description: The domain of a mapping. (Contributed by NM, 28-Jul-2008.) |
Ref | Expression |
---|---|
fdmi.1 | ⊢ 𝐹:𝐴⟶𝐵 |
Ref | Expression |
---|---|
fdmi | ⊢ dom 𝐹 = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fdmi.1 | . 2 ⊢ 𝐹:𝐴⟶𝐵 | |
2 | fdm 5166 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ dom 𝐹 = 𝐴 |
Colors of variables: wff set class |
Syntax hints: = wceq 1289 dom cdm 4438 ⟶wf 5011 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 |
This theorem depends on definitions: df-bi 115 df-fn 5018 df-f 5019 |
This theorem is referenced by: eluzel2 9024 inftonninf 9847 |
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