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Theorem f1fun 6262
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 6261 . 2 (𝐹:𝐴1-1𝐵𝐹 Fn 𝐴)
2 fnfun 6147 . 2 (𝐹 Fn 𝐴 → Fun 𝐹)
31, 2syl 17 1 (𝐹:𝐴1-1𝐵 → Fun 𝐹)
Colors of variables: wff setvar class
Syntax hints:  wi 4  Fun wfun 6041   Fn wfn 6042  1-1wf1 6044
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 197  df-an 385  df-fn 6050  df-f 6051  df-f1 6052
This theorem is referenced by:  f1cocnv2  6323  f1o2ndf1  7451  fnwelem  7458  f1dmvrnfibi  8413  fsuppco  8470  ackbij1b  9251  fin23lem31  9355  fin1a2lem6  9417  hashimarn  13417  gsumval3lem1  18504  gsumval3lem2  18505  usgrfun  26250  trlsegvdeglem6  27375  elhf  32585
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