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Theorem fndmu 5361
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 5359 . 2  |-  ( F  Fn  A  ->  dom  F  =  A )
2 fndm 5359 . 2  |-  ( F  Fn  B  ->  dom  F  =  B )
31, 2sylan9req 2349 1  |-  ( ( F  Fn  A  /\  F  Fn  B )  ->  A  =  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    = wceq 1632   dom cdm 4705    Fn wfn 5266
This theorem is referenced by:  fodmrnu  5475  0fz1  10829  grporn  20895  vcoprnelem  21150  hon0  22389
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-cleq 2289  df-fn 5274
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