Theorem eltpi 3570

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 3569	. 2 |- ( A e. { B , C , D } -> ( A e. { B , C , D } <-> ( A = B \/ A = C \/ A = D ) ) )
2	1	ibi 175	1 |- ( A e. { B , C , D } -> ( A = B \/ A = C \/ A = D ) )

Syntax hints:   -> wi 4   \/ w3o 961   = wceq 1331   e. wcel 1480   {ctp 3529

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-3or 963  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-tp 3535

This theorem is referenced by: (None)