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Theorem f1oeq123d 5148
 Description: Equality deduction for one-to-one onto functions. (Contributed by Mario Carneiro, 27-Jan-2017.)
Hypotheses
Ref Expression
f1eq123d.1
f1eq123d.2
f1eq123d.3
Assertion
Ref Expression
f1oeq123d

Proof of Theorem f1oeq123d
StepHypRef Expression
1 f1eq123d.1 . . 3
2 f1oeq1 5142 . . 3
31, 2syl 14 . 2
4 f1eq123d.2 . . 3
5 f1oeq2 5143 . . 3
64, 5syl 14 . 2
7 f1eq123d.3 . . 3
8 f1oeq3 5144 . . 3
97, 8syl 14 . 2
103, 6, 93bitrd 212 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285  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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  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-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-sn 3406  df-pr 3407  df-op 3409  df-br 3788  df-opab 3842  df-rel 4372  df-cnv 4373  df-co 4374  df-dm 4375  df-rn 4376  df-fun 4928  df-fn 4929  df-f 4930  df-f1 4931  df-fo 4932  df-f1o 4933 This theorem is referenced by:  f1oprg  5193
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