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Theorem fofun 5270
 Description: An onto mapping is a function. (Contributed by set.mm contributors, 29-Mar-2008.)
Assertion
Ref Expression
fofun (F:AontoB → Fun F)

Proof of Theorem fofun
StepHypRef Expression
1 fof 5269 . 2 (F:AontoBF:A–→B)
2 ffun 5225 . 2 (F:A–→B → Fun F)
31, 2syl 15 1 (F:AontoB → Fun F)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  Fun wfun 4775  –→wf 4777  –onto→wfo 4779 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-fn 4790  df-f 4791  df-fo 4793 This theorem is referenced by:  foimacnv  5303  resdif  5306
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