MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  fndmu Structured version   Unicode version

Theorem fndmu 5548
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 5546 . 2  |-  ( F  Fn  A  ->  dom  F  =  A )
2 fndm 5546 . 2  |-  ( F  Fn  B  ->  dom  F  =  B )
31, 2sylan9req 2491 1  |-  ( ( F  Fn  A  /\  F  Fn  B )  ->  A  =  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    = wceq 1653   dom cdm 4880    Fn wfn 5451
This theorem is referenced by:  fodmrnu  5663  0fz1  11076  grporn  21802  vcoprnelem  22059  hon0  23298  2ffzoeq  28151
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-cleq 2431  df-fn 5459
  Copyright terms: Public domain W3C validator