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Theorem f1ofun 5289
Description: A one-to-one onto mapping is a function. (Contributed by set.mm contributors, 12-Dec-2003.)
Assertion
Ref Expression
f1ofun (F:A1-1-ontoB → Fun F)

Proof of Theorem f1ofun
StepHypRef Expression
1 f1ofn 5288 . 2 (F:A1-1-ontoBF Fn A)
2 fnfun 5181 . 2 (F Fn A → Fun F)
31, 2syl 15 1 (F:A1-1-ontoB → Fun F)
Colors of variables: wff setvar class
Syntax hints:  wi 4  Fun wfun 4775   Fn wfn 4776  1-1-ontowf1o 4780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-fn 4790  df-f 4791  df-f1 4792  df-f1o 4794
This theorem is referenced by:  f1ococnv2  5309  enpw1  6062  sbthlem3  6205
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