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Theorem fndmu 6172
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 6170 . 2 (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
2 fndm 6170 . 2 (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵)
31, 2sylan9req 2820 1 ((𝐹 Fn 𝐴𝐹 Fn 𝐵) → 𝐴 = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384   = wceq 1652  dom cdm 5279   Fn wfn 6065
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1875  df-cleq 2758  df-fn 6073
This theorem is referenced by:  fodmrnu  6308  0fz1  12573  lmodfopnelem1  19182  grporn  27853  hon0  29129  2ffzoeq  42096
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