Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  elpr2 Unicode version

Theorem elpr2 3397
 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 3395 . . 3
21ibi 165 . 2
3 elpr2.1 . . . . . 6
4 eleq1 2100 . . . . . 6
53, 4mpbiri 157 . . . . 5
6 elpr2.2 . . . . . 6
7 eleq1 2100 . . . . . 6
86, 7mpbiri 157 . . . . 5
95, 8jaoi 636 . . . 4
10 elprg 3395 . . . 4
119, 10syl 14 . . 3
1211ibir 166 . 2
132, 12impbii 117 1
 Colors of variables: wff set class Syntax hints:   wb 98   wo 629   wceq 1243   wcel 1393  cvv 2557  cpr 3376 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382 This theorem is referenced by:  elxr  8696
 Copyright terms: Public domain W3C validator