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Theorem fodmrnu 5808
 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 5802 . . 3
2 fofn 5802 . . 3
3 fndmu 5687 . . 3
41, 2, 3syl2an 477 . 2
5 forn 5803 . . 3
6 forn 5803 . . 3
75, 6sylan9req 2519 . 2
84, 7jca 532 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  rancrn 5005  Fnwfn 5588  -onto->wfo 5591 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-in 3482  df-ss 3489  df-fn 5596  df-f 5597  df-fo 5599
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