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Theorem fndmu 5109
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 5107 . 2 (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
2 fndm 5107 . 2 (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵)
31, 2sylan9req 2141 1 ((𝐹 Fn 𝐴𝐹 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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