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Theorem f1ofn 5155
Description: A one-to-one onto mapping is function on its domain. (Contributed by NM, 12-Dec-2003.)
Assertion
Ref Expression
f1ofn (𝐹:𝐴1-1-onto𝐵𝐹 Fn 𝐴)

Proof of Theorem f1ofn
StepHypRef Expression
1 f1of 5154 . 2 (𝐹:𝐴1-1-onto𝐵𝐹:𝐴𝐵)
2 ffn 5074 . 2 (𝐹:𝐴𝐵𝐹 Fn 𝐴)
31, 2syl 14 1 (𝐹:𝐴1-1-onto𝐵𝐹 Fn 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   Fn wfn 4925  wf 4926  1-1-ontowf1o 4929
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-f 4934  df-f1 4935  df-f1o 4937
This theorem is referenced by:  f1ofun  5156  f1odm  5158  isocnv2  5480  isoini  5485  isoselem  5487  bren  6259  en1  6310  phplem4  6349  phplem4on  6360  dif1en  6368  supisolem  6412  ordiso2  6415
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