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Theorem fofun 5358
 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 5357 . 2 (𝐹:𝐴onto𝐵𝐹:𝐴𝐵)
2 ffun 5287 . 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 5129  ⟶wf 5131  –onto→wfo 5133 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-11 1483  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-in 3084  df-ss 3091  df-fn 5138  df-f 5139  df-fo 5141 This theorem is referenced by:  foimacnv  5397  resdif  5401  fococnv2  5405  fornex  6025  ctssdccl  7013  suplocexprlem2b  7575  suplocexprlemmu  7579  suplocexprlemdisj  7581  suplocexprlemloc  7582  suplocexprlemub  7584  suplocexprlemlub  7585  ennnfonelemex  11999  ctinf  12015
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