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Theorem fndmu 5028
Description: A function has a unique domain. (Contributed by NM, 11-Aug-1994.)
Assertion
Ref Expression
fndmu ((𝐹 Fn 𝐴𝐹 Fn 𝐵) → 𝐴 = 𝐵)

Proof of Theorem fndmu
StepHypRef Expression
1 fndm 5026 . 2 (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
2 fndm 5026 . 2 (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵)
31, 2sylan9req 2109 1 ((𝐹 Fn 𝐴𝐹 Fn 𝐵) → 𝐴 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101   = wceq 1259  dom cdm 4373   Fn wfn 4925
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-4 1416  ax-17 1435  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-fn 4933
This theorem is referenced by:  fodmrnu  5142  tfrlemisucaccv  5970  0fz1  9011
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