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Theorem fodmrnu 5365
 Description: An onto function has unique domain and range. (Contributed by NM, 5-Nov-2006.)
Assertion
Ref Expression
fodmrnu

Proof of Theorem fodmrnu
StepHypRef Expression
1 fofn 5359 . . 3
2 fofn 5359 . . 3
3 fndmu 5236 . . 3
41, 2, 3syl2an 287 . 2
5 forn 5360 . . 3
6 forn 5360 . . 3
75, 6sylan9req 2195 . 2
84, 7jca 304 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1332   crn 4552   wfn 5130  wfo 5133 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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-11 1483  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-in 3084  df-ss 3091  df-fn 5138  df-f 5139  df-fo 5141 This theorem is referenced by: (None)
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