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Theorem dffo2 5660
 Description: Alternate definition of an onto function. (Contributed by NM, 22-Mar-2006.)
Assertion
Ref Expression
dffo2

Proof of Theorem dffo2
StepHypRef Expression
1 fof 5656 . . 3
2 forn 5659 . . 3
31, 2jca 520 . 2
4 ffn 5594 . . 3
5 df-fo 5463 . . . 4
65biimpri 199 . . 3
74, 6sylan 459 . 2
83, 7impbii 182 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1653   crn 4882   wfn 5452  wf 5453  wfo 5455 This theorem is referenced by:  foco  5666  foconst  5667  dff1o5  5686  dffo3  5887  dffo4  5888  exfo  5890  fo1stres  6373  fo2ndres  6374  fo2ndf  6456  cantnf  7652  hsmexlem2  8312  1fv  11125  setcepi  14248  odf1o1  15211  efgsfo  15376  pjfo  16947  xrhmeo  18976  fargshiftfo  21630  grpofo  21792  cnpcon  24922  lnmepi  27174 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-in 3329  df-ss 3336  df-f 5461  df-fo 5463
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