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Theorem dff1o5 5135
 Description: Alternate definition of one-to-one onto function. (Contributed by NM, 10-Dec-2003.) (Proof shortened by Andrew Salmon, 22-Oct-2011.)
Assertion
Ref Expression
dff1o5

Proof of Theorem dff1o5
StepHypRef Expression
1 df-f1o 4909 . 2
2 f1f 5092 . . . . 5
32biantrurd 289 . . . 4
4 dffo2 5110 . . . 4
53, 4syl6rbbr 188 . . 3
65pm5.32i 427 . 2
71, 6bitri 173 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   wceq 1243   crn 4346  wf 4898  wf1 4899  wfo 4900  wf1o 4901 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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931  df-f 4906  df-f1 4907  df-fo 4908  df-f1o 4909 This theorem is referenced by:  f1orescnv  5142  frec2uzf1od  9192
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