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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 5107 | . 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴) | |
2 | fndm 5107 | . 2 ⊢ (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵) | |
3 | 1, 2 | sylan9req 2141 | 1 ⊢ ((𝐹 Fn 𝐴 ∧ 𝐹 Fn 𝐵) → 𝐴 = 𝐵) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 = wceq 1289 dom cdm 4436 Fn wfn 5005 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1381 ax-gen 1383 ax-4 1445 ax-17 1464 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-cleq 2081 df-fn 5013 |
This theorem is referenced by: fodmrnu 5235 tfrlemisucaccv 6082 tfr1onlemsucaccv 6098 tfrcllemsucaccv 6111 0fz1 9449 |
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