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Theorem fofn 5051
 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 5049 . 2 (𝐹:AontoB𝐹:AB)
2 ffn 4989 . 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 4840  ⟶wf 4841  –onto→wfo 4843 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925  df-f 4849  df-fo 4851 This theorem is referenced by:  fodmrnu  5057  foun  5088  fo00  5105  cbvfo  5368  cbvexfo  5369  foeqcnvco  5373  1stcof  5732  2ndcof  5733  1stexg  5736  2ndexg  5737  df1st2  5782  df2nd2  5783  1stconst  5784  2ndconst  5785
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