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Theorem f1ofn 5127
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 5126 . 2 (𝐹:𝐴1-1-onto𝐵𝐹:𝐴𝐵)
2 ffn 5046 . 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 4897  wf 4898  1-1-ontowf1o 4901
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99
This theorem depends on definitions:  df-bi 110  df-f 4906  df-f1 4907  df-f1o 4909
This theorem is referenced by:  f1ofun  5128  f1odm  5130  isocnv2  5452  isoini  5457  isoselem  5459  bren  6228  en1  6279  phplem4  6318  phplem4on  6329  dif1en  6337  ordiso2  6357
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