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Theorem dff1o3 5157
 Description: Alternate definition of one-to-one onto function. (Contributed by NM, 25-Mar-1998.) (Proof shortened by Andrew Salmon, 22-Oct-2011.)
Assertion
Ref Expression
dff1o3

Proof of Theorem dff1o3
StepHypRef Expression
1 3anan32 931 . 2
2 dff1o2 5156 . 2
3 df-fo 4932 . . 3
43anbi1i 446 . 2
51, 2, 43bitr4i 210 1
 Colors of variables: wff set class Syntax hints:   wa 102   wb 103   w3a 920   wceq 1285  ccnv 4364   crn 4366   wfun 4920   wfn 4921  wfo 4924  wf1o 4925 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987  df-f 4930  df-f1 4931  df-fo 4932  df-f1o 4933 This theorem is referenced by:  f1ofo  5158  resdif  5173  f11o  5184  f1opw  5732  1stconst  5867  2ndconst  5868  f1o2ndf1  5874  ssdomg  6317  phplem4  6380  phplem4on  6392
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