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Theorem eltp 3582
 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 3580 . 2
31, 2ax-mp 10 1
 Colors of variables: wff set class Syntax hints:   wb 178   w3o 938   wceq 1619   wcel 1621  cvv 2727  ctp 3546 This theorem is referenced by:  dftp2  3583  tpid1  3643  tpid2  3644  tpid3  3646  brtp  23276  axsltsolem1  23489  bpoly3  23967  fnckle  25211 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 940  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-un 3083  df-sn 3550  df-pr 3551  df-tp 3552
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