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Theorem dff1o3 5373
 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 973 . 2
2 dff1o2 5372 . 2
3 df-fo 5129 . . 3
43anbi1i 453 . 2
51, 2, 43bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   w3a 962   wceq 1331  ccnv 4538   crn 4540   wfun 5117   wfn 5118  wfo 5121  wf1o 5122 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 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084  df-f 5127  df-f1 5128  df-fo 5129  df-f1o 5130 This theorem is referenced by:  f1ofo  5374  resdif  5389  f11o  5400  f1opw  5977  1stconst  6118  2ndconst  6119  f1o2ndf1  6125  ssdomg  6672  phplem4  6749  phplem4on  6761
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