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Theorem tpss 3871
 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 3437 . 2
2 df-3an 936 . . 3
3 tpss.1 . . . . 5
4 tpss.2 . . . . 5
53, 4prss 3861 . . . 4
6 tpss.3 . . . . 5
76snss 3838 . . . 4
85, 7anbi12i 678 . . 3
92, 8bitri 240 . 2
10 df-tp 3743 . . 3
1110sseq1i 3295 . 2
121, 9, 113bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358   w3a 934   wcel 1710  cvv 2859   cun 3207   wss 3257  csn 3737  cpr 3738  ctp 3739 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-ss 3259  df-sn 3741  df-pr 3742  df-tp 3743 This theorem is referenced by: (None)
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