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Theorem tpss 3529
 Description: A triplet of elements of a class is a subset of the class. (Contributed by NM, 9-Apr-1994.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Hypotheses
Ref Expression
tpss.1
tpss.2
tpss.3
Assertion
Ref Expression
tpss

Proof of Theorem tpss
StepHypRef Expression
1 unss 3117 . 2
2 df-3an 887 . . 3
3 tpss.1 . . . . 5
4 tpss.2 . . . . 5
53, 4prss 3520 . . . 4
6 tpss.3 . . . . 5
76snss 3494 . . . 4
85, 7anbi12i 433 . . 3
92, 8bitri 173 . 2
10 df-tp 3383 . . 3
1110sseq1i 2969 . 2
121, 9, 113bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   w3a 885   wcel 1393  cvv 2557   cun 2915   wss 2917  csn 3375  cpr 3376  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-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-tp 3383 This theorem is referenced by: (None)
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