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Theorem fndmu 6675
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 6671 . 2 (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
2 fndm 6671 . 2 (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵)
31, 2sylan9req 2798 1 ((𝐹 Fn 𝐴𝐹 Fn 𝐵) → 𝐴 = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395   = wceq 1540  dom cdm 5685   Fn wfn 6556
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2729  df-fn 6564
This theorem is referenced by:  fodmrnu  6828  0fz1  13584  lmodfopnelem1  20896  grporn  30540  hon0  31812  2ffzoeq  47339
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