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Theorem fndmu 6105
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 6103 . 2 (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
2 fndm 6103 . 2 (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵)
31, 2sylan9req 2779 1 ((𝐹 Fn 𝐴𝐹 Fn 𝐵) → 𝐴 = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383   = wceq 1596  dom cdm 5218   Fn wfn 5996
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-ext 2704
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1818  df-cleq 2717  df-fn 6004
This theorem is referenced by:  fodmrnu  6236  0fz1  12475  lmodfopnelem1  19022  grporn  27605  hon0  28882  2ffzoeq  41765
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