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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 5222 | . 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴) | |
2 | fndm 5222 | . 2 ⊢ (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵) | |
3 | 1, 2 | sylan9req 2193 | 1 ⊢ ((𝐹 Fn 𝐴 ∧ 𝐹 Fn 𝐵) → 𝐴 = 𝐵) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 = wceq 1331 dom cdm 4539 Fn wfn 5118 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-4 1487 ax-17 1506 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-cleq 2132 df-fn 5126 |
This theorem is referenced by: fodmrnu 5353 tfrlemisucaccv 6222 tfr1onlemsucaccv 6238 tfrcllemsucaccv 6251 0fz1 9825 |
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