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Theorem tpssi 3654
 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

Proof of Theorem tpssi
StepHypRef Expression
1 df-tp 3503 . 2
2 prssi 3646 . . . 4
323adant3 984 . . 3
4 snssi 3632 . . . 4
543ad2ant3 987 . . 3
63, 5unssd 3220 . 2
71, 6eqsstrid 3111 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 945   wcel 1463   cun 3037   wss 3039  csn 3495  cpr 3496  ctp 3497 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-sn 3501  df-pr 3502  df-tp 3503 This theorem is referenced by: (None)
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