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Theorem fndmu 5051
Description: A function has a unique domain. (Contributed by NM, 11-Aug-1994.)
Assertion
Ref Expression
fndmu  |-  ( ( F  Fn  A  /\  F  Fn  B )  ->  A  =  B )

Proof of Theorem fndmu
StepHypRef Expression
1 fndm 5049 . 2  |-  ( F  Fn  A  ->  dom  F  =  A )
2 fndm 5049 . 2  |-  ( F  Fn  B  ->  dom  F  =  B )
31, 2sylan9req 2136 1  |-  ( ( F  Fn  A  /\  F  Fn  B )  ->  A  =  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    = wceq 1285   dom cdm 4391    Fn wfn 4947
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-fn 4955
This theorem is referenced by:  fodmrnu  5166  tfrlemisucaccv  5995  tfr1onlemsucaccv  6011  tfrcllemsucaccv  6024  0fz1  9210
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