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Theorem f1orn 5831
Description: A one-to-one function maps onto its range. (Contributed by NM, 13-Aug-2004.)
Assertion
Ref Expression
f1orn

Proof of Theorem f1orn
StepHypRef Expression
1 dff1o2 5826 . 2
2 eqid 2457 . . 3
3 df-3an 975 . . 3
42, 3mpbiran2 919 . 2
51, 4bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  `'ccnv 5003  rancrn 5005  Funwfun 5587  Fnwfn 5588  -1-1-onto->wf1o 5592
This theorem is referenced by:  f1f1orn  5832  infdifsn  8094  efopnlem2  23038
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-3an 975  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-f 5597  df-f1 5598  df-fo 5599  df-f1o 5600
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