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Theorem fndmu 6657
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 6653 . 2 (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
2 fndm 6653 . 2 (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵)
31, 2sylan9req 2794 1 ((𝐹 Fn 𝐴𝐹 Fn 𝐵) → 𝐴 = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397   = wceq 1542  dom cdm 5677   Fn wfn 6539
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-cleq 2725  df-fn 6547
This theorem is referenced by:  fodmrnu  6814  0fz1  13521  lmodfopnelem1  20508  grporn  29774  hon0  31046  2ffzoeq  46036
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