Theorem dftp2 3625

Description: Alternate definition of unordered triple of classes. Special case of Definition 5.3 of [TakeutiZaring] p. 16. (Contributed by NM, 8-Apr-1994.)

Assertion

Ref	Expression
dftp2	|- { A , B , C } = { x | ( x = A \/ x = B \/ x = C ) }

Distinct variable groups:   x, A   x, B   x, C

Proof of Theorem dftp2

Step	Hyp	Ref	Expression
1		vex 2729	. . 3 |- x e. _V
2	1	eltp 3624	. 2 |- ( x e. { A , B , C } <-> ( x = A \/ x = B \/ x = C ) )
3	2	abbi2i 2281	1 |- { A , B , C } = { x | ( x = A \/ x = B \/ x = C ) }

Syntax hints:   \/ w3o 967   = wceq 1343   {cab 2151   {ctp 3578

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 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-3or 969  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-un 3120  df-sn 3582  df-pr 3583  df-tp 3584

This theorem is referenced by:  tprot  3669  tpid3g  3691