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Theorem tpprceq3 4170
Description: An unordered triple is an unordered pair if one of its elements is a proper class or is identical with another element. (Contributed by Alexander van der Vekens, 6-Oct-2017.)
Assertion
Ref Expression
tpprceq3

Proof of Theorem tpprceq3
StepHypRef Expression
1 ianor 488 . 2
2 tprot 4125 . . . 4
3 df-tp 4034 . . . . 5
4 prprc2 4141 . . . . . . 7
54uneq1d 3656 . . . . . 6
6 df-pr 4032 . . . . . . 7
7 prcom 4108 . . . . . . 7
86, 7eqtr3i 2488 . . . . . 6
95, 8syl6eq 2514 . . . . 5
103, 9syl5eq 2510 . . . 4
112, 10syl5eq 2510 . . 3
12 nne 2658 . . . 4
13 tppreq3 4135 . . . . 5
1413eqcoms 2469 . . . 4
1512, 14sylbi 195 . . 3
1611, 15jaoi 379 . 2
171, 16sylbi 195 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652   cvv 3109  u.cun 3473  {csn 4029  {cpr 4031  {ctp 4033
This theorem is referenced by:  tppreqb  4171  1to3vfriswmgra  25007
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-nul 3785  df-sn 4030  df-pr 4032  df-tp 4034
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