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Theorem tpssi 3521
Description: A triple of elements of a class is a subset of the class. (Contributed by Alexander van der Vekens, 1-Feb-2018.)
Assertion
Ref Expression
tpssi  D  D  C  D  { ,  ,  C }  C_  D

Proof of Theorem tpssi
StepHypRef Expression
1 df-tp 3375 . 2  { ,  ,  C }  { ,  }  u.  { C }
2 prssi 3513 . . . 4  D  D  { ,  }  C_  D
323adant3 923 . . 3  D  D  C  D  { ,  }  C_  D
4 snssi 3499 . . . 4  C  D  { C }  C_  D
543ad2ant3 926 . . 3  D  D  C  D  { C }  C_  D
63, 5unssd 3113 . 2  D  D  C  D  { ,  }  u.  { C }  C_  D
71, 6syl5eqss 2983 1  D  D  C  D  { ,  ,  C }  C_  D
Colors of variables: wff set class
Syntax hints:   wi 4   w3a 884   wcel 1390    u. cun 2909    C_ wss 2911   {csn 3367   {cpr 3368   {ctp 3369
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-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
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-sn 3373  df-pr 3374  df-tp 3375
This theorem is referenced by: (None)
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