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Theorem eltp 3418
 Description: A member of an unordered triple of classes is one of them. Special case of Exercise 1 of [TakeutiZaring] p. 17. (Contributed by NM, 8-Apr-1994.) (Revised by Mario Carneiro, 11-Feb-2015.)
Hypothesis
Ref Expression
eltp.1
Assertion
Ref Expression
eltp

Proof of Theorem eltp
StepHypRef Expression
1 eltp.1 . 2
2 eltpg 3416 . 2
31, 2ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wb 98   w3o 884   wceq 1243   wcel 1393  cvv 2557  ctp 3377 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-3or 886  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-sn 3381  df-pr 3382  df-tp 3383 This theorem is referenced by:  dftp2  3419  tpid1  3481  tpid2  3482  tpid3  3484
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