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Theorem elpr2 3563
 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 3561 . . 3
21ibi 234 . 2
3 elpr2.1 . . . . . 6
4 eleq1 2313 . . . . . 6
53, 4mpbiri 226 . . . . 5
6 elpr2.2 . . . . . 6
7 eleq1 2313 . . . . . 6
86, 7mpbiri 226 . . . . 5
95, 8jaoi 370 . . . 4
10 elprg 3561 . . . 4
119, 10syl 17 . . 3
1211ibir 235 . 2
132, 12impbii 182 1
 Colors of variables: wff set class Syntax hints:   wb 178   wo 359   wceq 1619   wcel 1621  cvv 2727  cpr 3545 This theorem is referenced by:  elxr  10337  nofv  23478 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-un 3083  df-sn 3550  df-pr 3551
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