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Theorem f1odm 5181
Description: The domain of a one-to-one onto mapping. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1odm  |-  ( F : A -1-1-onto-> B  ->  dom  F  =  A )

Proof of Theorem f1odm
StepHypRef Expression
1 f1ofn 5178 . 2  |-  ( F : A -1-1-onto-> B  ->  F  Fn  A )
2 fndm 5049 . 2  |-  ( F  Fn  A  ->  dom  F  =  A )
31, 2syl 14 1  |-  ( F : A -1-1-onto-> B  ->  dom  F  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285   dom cdm 4391    Fn wfn 4947   -1-1-onto->wf1o 4951
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115  df-fn 4955  df-f 4956  df-f1 4957  df-f1o 4959
This theorem is referenced by:  f1imacnv  5194  f1opw2  5757  xpcomco  6391  phplem4  6411  phplem4on  6423  dif1en  6435  djuun  6558  fihasheqf1oi  9864
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