Theorem eltpi 4229

Description: A member of an unordered triple of classes is one of them. (Contributed by Mario Carneiro, 11-Feb-2015.)

Assertion

Ref	Expression
eltpi	|- ( A e. { B , C , D } -> ( A = B \/ A = C \/ A = D ) )

Proof of Theorem eltpi

Step	Hyp	Ref	Expression
1		eltpg 4227	. 2 |- ( A e. { B , C , D } -> ( A e. { B , C , D } <-> ( A = B \/ A = C \/ A = D ) ) )
2	1	ibi 256	1 |- ( A e. { B , C , D } -> ( A = B \/ A = C \/ A = D ) )

Syntax hints:   -> wi 4   \/ w3o 1036   = wceq 1483   e. wcel 1990   {ctp 4181

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1038  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-sn 4178  df-pr 4180  df-tp 4182

This theorem is referenced by:  prm23lt5  15519  perfectlem2  24955  zabsle1  25021  sgnmulsgn  30611  sgnmulsgp  30612  kur14lem7  31194  fmtnofz04prm  41489  perfectALTVlem2  41631