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Theorem elpr2 4048
Description: A member of an unordered pair of classes is one or the other of them. Exercise 1 of [TakeutiZaring] p. 15. (Contributed by NM, 14-Oct-2005.)
Hypotheses
Ref Expression
elpr2.1
elpr2.2
Assertion
Ref Expression
elpr2

Proof of Theorem elpr2
StepHypRef Expression
1 elprg 4045 . . 3
21ibi 241 . 2
3 elpr2.1 . . . . . 6
4 eleq1 2529 . . . . . 6
53, 4mpbiri 233 . . . . 5
6 elpr2.2 . . . . . 6
7 eleq1 2529 . . . . . 6
86, 7mpbiri 233 . . . . 5
95, 8jaoi 379 . . . 4
10 elprg 4045 . . . 4
119, 10syl 16 . . 3
1211ibir 242 . 2
132, 12impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  \/wo 368  =wceq 1395  e.wcel 1818   cvv 3109  {cpr 4031
This theorem is referenced by:  elxr  11354  nofv  29417  bj-elopg  34602
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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-sn 4030  df-pr 4032
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