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Theorem foeq123d 5122
 Description: Equality deduction for onto functions. (Contributed by Mario Carneiro, 27-Jan-2017.)
Hypotheses
Ref Expression
f1eq123d.1
f1eq123d.2
f1eq123d.3
Assertion
Ref Expression
foeq123d

Proof of Theorem foeq123d
StepHypRef Expression
1 f1eq123d.1 . . 3
2 foeq1 5102 . . 3
31, 2syl 14 . 2
4 f1eq123d.2 . . 3
5 foeq2 5103 . . 3
64, 5syl 14 . 2
7 f1eq123d.3 . . 3
8 foeq3 5104 . . 3
97, 8syl 14 . 2
103, 6, 93bitrd 203 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243  wfo 4900 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-rel 4352  df-cnv 4353  df-co 4354  df-dm 4355  df-rn 4356  df-fun 4904  df-fn 4905  df-fo 4908 This theorem is referenced by: (None)
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