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Theorem f1ofun 5155
Description: A one-to-one onto mapping is a function. (Contributed by NM, 12-Dec-2003.)
Assertion
Ref Expression
f1ofun (𝐹:𝐴1-1-onto𝐵 → Fun 𝐹)

Proof of Theorem f1ofun
StepHypRef Expression
1 f1ofn 5154 . 2 (𝐹:𝐴1-1-onto𝐵𝐹 Fn 𝐴)
2 fnfun 5023 . 2 (𝐹 Fn 𝐴 → Fun 𝐹)
31, 2syl 14 1 (𝐹:𝐴1-1-onto𝐵 → Fun 𝐹)
Colors of variables: wff set class
Syntax hints:  wi 4  Fun wfun 4923   Fn wfn 4924  1-1-ontowf1o 4928
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103
This theorem depends on definitions:  df-bi 114  df-fn 4932  df-f 4933  df-f1 4934  df-f1o 4936
This theorem is referenced by:  f1orel  5156  f1oresrab  5356  isose  5487  f1opw  5734  xpcomco  6330
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