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Mirrors > Home > ILE Home > Th. List > fndmu | GIF version |
Description: A function has a unique domain. (Contributed by NM, 11-Aug-1994.) |
Ref | Expression |
---|---|
fndmu | ⊢ ((𝐹 Fn 𝐴 ∧ 𝐹 Fn 𝐵) → 𝐴 = 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fndm 5334 | . 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴) | |
2 | fndm 5334 | . 2 ⊢ (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵) | |
3 | 1, 2 | sylan9req 2243 | 1 ⊢ ((𝐹 Fn 𝐴 ∧ 𝐹 Fn 𝐵) → 𝐴 = 𝐵) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 = wceq 1364 dom cdm 4644 Fn wfn 5230 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-4 1521 ax-17 1537 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-cleq 2182 df-fn 5238 |
This theorem is referenced by: fodmrnu 5465 tfrlemisucaccv 6351 tfr1onlemsucaccv 6367 tfrcllemsucaccv 6380 0fz1 10077 lmodfopnelem1 13657 |
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