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Theorem fndmu 5317
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 5315 . 2 (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
2 fndm 5315 . 2 (𝐹 Fn 𝐵 → dom 𝐹 = 𝐵)
31, 2sylan9req 2231 1 ((𝐹 Fn 𝐴𝐹 Fn 𝐵) → 𝐴 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104   = wceq 1353  dom cdm 4626   Fn wfn 5211
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-4 1510  ax-17 1526  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-fn 5219
This theorem is referenced by:  fodmrnu  5446  tfrlemisucaccv  6325  tfr1onlemsucaccv  6341  tfrcllemsucaccv  6354  0fz1  10044
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