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Theorem fofun 5132
 Description: An onto mapping is a function. (Contributed by NM, 29-Mar-2008.)
Assertion
Ref Expression
fofun (𝐹:𝐴onto𝐵 → Fun 𝐹)

Proof of Theorem fofun
StepHypRef Expression
1 fof 5131 . 2 (𝐹:𝐴onto𝐵𝐹:𝐴𝐵)
2 ffun 5073 . 2 (𝐹:𝐴𝐵 → Fun 𝐹)
31, 2syl 14 1 (𝐹:𝐴onto𝐵 → Fun 𝐹)
 Colors of variables: wff set class Syntax hints:   → wi 4  Fun wfun 4920  ⟶wf 4922  –onto→wfo 4924 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987  df-fn 4929  df-f 4930  df-fo 4932 This theorem is referenced by:  foimacnv  5169  resdif  5173  fococnv2  5177  fornex  5767
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