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Theorem f1fun 5423
Description: A one-to-one mapping is a function. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1fun (𝐹:𝐴1-1𝐵 → Fun 𝐹)

Proof of Theorem f1fun
StepHypRef Expression
1 f1fn 5422 . 2 (𝐹:𝐴1-1𝐵𝐹 Fn 𝐴)
2 fnfun 5312 . 2 (𝐹 Fn 𝐴 → Fun 𝐹)
31, 2syl 14 1 (𝐹:𝐴1-1𝐵 → Fun 𝐹)
Colors of variables: wff set class
Syntax hints:  wi 4  Fun wfun 5209   Fn wfn 5210  1-1wf1 5212
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106
This theorem depends on definitions:  df-bi 117  df-fn 5218  df-f 5219  df-f1 5220
This theorem is referenced by:  f1cocnv2  5488  f1o2ndf1  6226  f1dmvrnfibi  6940  djuinj  7102
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