Theorem eltpi 3771

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 3770	. 2 |- (A e. {B, C, D} -> (A e. {B, C, D} <-> (A = B \/ A = C \/ A = D)))
2	1	ibi 232	1 |- (A e. {B, C, D} -> (A = B \/ A = C \/ A = D))

Syntax hints:   -> wi 4   \/ w3o 933   = wceq 1642   e. wcel 1710  {ctp 3740

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-v 2862  df-nin 3212  df-compl 3213  df-un 3215  df-sn 3742  df-pr 3743  df-tp 3744

This theorem is referenced by: (None)