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Theorem fofn 5136
 Description: An onto mapping is a function on its domain. (Contributed by NM, 16-Dec-2008.)
Assertion
Ref Expression
fofn (𝐹:𝐴onto𝐵𝐹 Fn 𝐴)

Proof of Theorem fofn
StepHypRef Expression
1 fof 5134 . 2 (𝐹:𝐴onto𝐵𝐹:𝐴𝐵)
2 ffn 5074 . 2 (𝐹:𝐴𝐵𝐹 Fn 𝐴)
31, 2syl 14 1 (𝐹:𝐴onto𝐵𝐹 Fn 𝐴)
 Colors of variables: wff set class Syntax hints:   → wi 4   Fn wfn 4925  ⟶wf 4926  –onto→wfo 4928 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959  df-f 4934  df-fo 4936 This theorem is referenced by:  fodmrnu  5142  foun  5173  fo00  5190  cbvfo  5453  cbvexfo  5454  foeqcnvco  5458  1stcof  5818  2ndcof  5819  1stexg  5822  2ndexg  5823  df1st2  5868  df2nd2  5869  1stconst  5870  2ndconst  5871
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