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Theorem otth2 3969
 Description: Ordered triple theorem, with triple express with ordered pairs. (Contributed by NM, 1-May-1995.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
otth.1
otth.2
otth.3
Assertion
Ref Expression
otth2

Proof of Theorem otth2
StepHypRef Expression
1 otth.1 . . . 4
2 otth.2 . . . 4
31, 2opth 3965 . . 3
43anbi1i 431 . 2
5 opexgOLD 3956 . . . 4
61, 2, 5mp2an 402 . . 3
7 otth.3 . . 3
86, 7opth 3965 . 2
9 df-3an 886 . 2
104, 8, 93bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   w3a 884   wceq 1242   wcel 1390  cvv 2551  cop 3370 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376 This theorem is referenced by:  otth  3970  oprabid  5480  eloprabga  5533
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