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Theorem elpr2 3659
 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 3657 . . 3
21ibi 232 . 2
3 elpr2.1 . . . . . 6
4 eleq1 2343 . . . . . 6
53, 4mpbiri 224 . . . . 5
6 elpr2.2 . . . . . 6
7 eleq1 2343 . . . . . 6
86, 7mpbiri 224 . . . . 5
95, 8jaoi 368 . . . 4
10 elprg 3657 . . . 4
119, 10syl 15 . . 3
1211ibir 233 . 2
132, 12impbii 180 1
 Colors of variables: wff set class Syntax hints:   wb 176   wo 357   wceq 1623   wcel 1684  cvv 2788  cpr 3641 This theorem is referenced by:  elxr  10458  nofv  24311 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-sn 3646  df-pr 3647
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