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Theorem f1dm 5333
Description: The domain of a one-to-one mapping. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1dm  |-  ( F : A -1-1-> B  ->  dom  F  =  A )

Proof of Theorem f1dm
StepHypRef Expression
1 f1fn 5330 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fndm 5222 . 2  |-  ( F  Fn  A  ->  dom  F  =  A )
31, 2syl 14 1  |-  ( F : A -1-1-> B  ->  dom  F  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1331   dom cdm 4539    Fn wfn 5118   -1-1->wf1 5120
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem depends on definitions:  df-bi 116  df-fn 5126  df-f 5127  df-f1 5128
This theorem is referenced by:  fun11iun  5388  tposf12  6166  f1dmvrnfibi  6832  f1vrnfibi  6833  exmidfodomrlemim  7057  hmeoimaf1o  12493  exmidsbthrlem  13231
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