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Theorem elprg 3561
 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
StepHypRef Expression
1 eqeq1 2259 . . 3
2 eqeq1 2259 . . 3
31, 2orbi12d 693 . 2
4 dfpr2 3560 . 2
53, 4elab2g 2853 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wo 359   wceq 1619   wcel 1621  cpr 3545 This theorem is referenced by:  elpr  3562  elpr2  3563  elpri  3564  eltpg  3580  ifpr  3585  prid1g  3636  ordunpr  4508  cnsubrg  16264  atandm  20004  eupath2lem1  23072  repfuntw  24326 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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