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Theorem dff1o5 5376
 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 5130 . 2
2 f1f 5328 . . . . 5
32biantrurd 303 . . . 4
4 dffo2 5349 . . . 4
53, 4syl6rbbr 198 . . 3
65pm5.32i 449 . 2
71, 6bitri 183 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   wceq 1331   crn 4540  wf 5119  wf1 5120  wfo 5121  wf1o 5122 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 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084  df-f 5127  df-f1 5128  df-fo 5129  df-f1o 5130 This theorem is referenced by:  f1orescnv  5383  f1finf1o  6835  djuinr  6948  eninl  6982  eninr  6983  frec2uzf1od  10186  ennnfonelemex  11933  ennnfonelemen  11940  pwf1oexmid  13247
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