Theorem elpri 3440

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

Step	Hyp	Ref	Expression
1		elprg 3437	. 2 |- ( A e. { B , C } -> ( A e. { B , C } <-> ( A = B \/ A = C ) ) )
2	1	ibi 174	1 |- ( A e. { B , C } -> ( A = B \/ A = C ) )

Syntax hints:   -> wi 4   \/ wo 662   = wceq 1285   e. wcel 1434   {cpr 3418

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2987  df-sn 3423  df-pr 3424

This theorem is referenced by:  nelpri  3441  opth1  4020  0nelop  4032  ontr2exmid  4297  onintexmid  4344  reg3exmidlemwe  4350  funtpg  5002  ftpg  5400  acexmidlemcase  5559  2oconcl  6107  en2eqpr  6459  m1expcl2  9631  maxleim  10276  maxleast  10284  minmax  10297