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Theorem elpri 3826
Description: If a class is an element of a pair, then it is one of the two paired elements. (Contributed by Scott Fenton, 1-Apr-2011.)
Assertion
Ref Expression
elpri  |-  ( A  e.  { B ,  C }  ->  ( A  =  B  \/  A  =  C ) )

Proof of Theorem elpri
StepHypRef Expression
1 elprg 3823 . 2  |-  ( A  e.  { B ,  C }  ->  ( A  e.  { B ,  C }  <->  ( A  =  B  \/  A  =  C ) ) )
21ibi 233 1  |-  ( A  e.  { B ,  C }  ->  ( A  =  B  \/  A  =  C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 358    = wceq 1652    e. wcel 1725   {cpr 3807
This theorem is referenced by:  nelpri  3827  tppreqb  3931  opth1  4426  0nelop  4438  funtpg  5492  ftpg  5907  2oconcl  6738  cantnflem2  7635  m1expcl2  11391  bitsinv1lem  12941  xpscfv  13775  xpsfeq  13777  frgpuptinv  15391  frgpup3lem  15397  indiscld  17143  cnindis  17344  conclo  17466  txindis  17654  xpsxmetlem  18397  xpsmet  18400  ishl2  19312  recnprss  19779  recnperf  19780  dvlip2  19867  coseq0negpitopi  20399  pythag  20647  reasinsin  20724  scvxcvx  20812  perfectlem2  21002  lgslem4  21071  lgseisenlem2  21122  usgraedg4  21394  cusgrares  21469  2pthlem2  21584  vdgr1a  21665  konigsberg  21697  ex-pr  21726  elpreq  23987  kur14lem7  24886  wepwsolem  27053  m1expaddsub  27336  cnmsgnsubg  27349  ssrecnpr  27452  seff  27453  sblpnf  27454  expgrowthi  27465  dvconstbi  27466  sumpair  27620  refsum2cnlem1  27622  nelprd  27991
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-sn 3812  df-pr 3813
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