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Theorem f1oeq3 5144
 Description: Equality theorem for one-to-one onto functions. (Contributed by NM, 10-Feb-1997.)
Assertion
Ref Expression
f1oeq3

Proof of Theorem f1oeq3
StepHypRef Expression
1 f1eq3 5114 . . 3
2 foeq3 5129 . . 3
31, 2anbi12d 457 . 2
4 df-f1o 4933 . 2
5 df-f1o 4933 . 2
63, 4, 53bitr4g 221 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285  wf1 4923  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-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:  f1oeq23  5145  f1oeq123d  5148  f1ores  5166  resdif  5173  f1osng  5192  f1oresrab  5355  isoeq5  5470  isoini2  5483  bren  6287  xpcomf1o  6359  frechashgf1o  9499  sumeq1  10319
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