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Theorem f1ofn 5288
Description: A one-to-one onto mapping is function on its domain. (Contributed by set.mm contributors, 12-Dec-2003.)
Assertion
Ref Expression
f1ofn (F:A1-1-ontoBF Fn A)

Proof of Theorem f1ofn
StepHypRef Expression
1 f1of 5287 . 2 (F:A1-1-ontoBF:A–→B)
2 ffn 5223 . 2 (F:A–→BF Fn A)
31, 2syl 15 1 (F:A1-1-ontoBF Fn A)
Colors of variables: wff setvar class
Syntax hints:  wi 4   Fn wfn 4776  –→wf 4777  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-f 4791  df-f1 4792  df-f1o 4794
This theorem is referenced by:  f1ofun  5289  f1odm  5290  f1ofveu  5480  isomin  5496  isoini  5497  nenpw1pwlem2  6085
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