Theorem dftp2 3441

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 2604	. . 3 |- x e. _V
2	1	eltp 3440	. 2 |- ( x e. { A , B , C } <-> ( x = A \/ x = B \/ x = C ) )
3	2	abbi2i 2193	1 |- { A , B , C } = { x | ( x = A \/ x = B \/ x = C ) }

Syntax hints:   \/ w3o 918   = wceq 1284   {cab 2067   {ctp 3400

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 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-3or 920  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-un 2977  df-sn 3404  df-pr 3405  df-tp 3406

This theorem is referenced by:  tprot  3485  tpid3g  3505