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Theorem elprg 3580
 Description: A member of an unordered pair of classes is one or the other of them. Exercise 1 of [TakeutiZaring] p. 15, generalized. (Contributed by NM, 13-Sep-1995.)
Assertion
Ref Expression
elprg

Proof of Theorem elprg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq1 2164 . . 3
2 eqeq1 2164 . . 3
31, 2orbi12d 783 . 2
4 dfpr2 3579 . 2
53, 4elab2g 2859 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wo 698   wceq 1335   wcel 2128  cpr 3561 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567 This theorem is referenced by:  elpr  3581  elpr2  3582  elpri  3583  eldifpr  3587  eltpg  3604  prid1g  3663  preqr1g  3729  m1expeven  10448  maxclpr  11104  minmax  11111  minclpr  11118  xrminmax  11144
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