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Theorem f1f1orn 5080
Description: A one-to-one function maps one-to-one onto its range. (Contributed by NM, 4-Sep-2004.)
Assertion
Ref Expression
f1f1orn  F : -1-1->  F : -1-1-onto-> ran  F

Proof of Theorem f1f1orn
StepHypRef Expression
1 f1fn 5036 . 2  F : -1-1->  F  Fn
2 df-f1 4850 . . 3  F : -1-1->  F : -->  Fun  `' F
32simprbi 260 . 2  F : -1-1->  Fun  `' F
4 f1orn 5079 . 2  F : -1-1-onto-> ran  F  F  Fn  Fun  `' F
51, 3, 4sylanbrc 394 1  F : -1-1->  F : -1-1-onto-> ran  F
Colors of variables: wff set class
Syntax hints:   wi 4   `'ccnv 4287   ran crn 4289   Fun wfun 4839    Fn wfn 4840   -->wf 4841   -1-1->wf1 4842   -1-1-onto->wf1o 4844
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-3an 886  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-f1 4850  df-fo 4851  df-f1o 4852
This theorem is referenced by:  f1ores  5084  f1cnv  5093  f1cocnv1  5099  f1ocnvfvrneq  5365
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