Theorem dftp2 4231

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 3203	. . 3 |- x e. _V
2	1	eltp 4230	. 2 |- ( x e. { A , B , C } <-> ( x = A \/ x = B \/ x = C ) )
3	2	abbi2i 2738	1 |- { A , B , C } = { x | ( x = A \/ x = B \/ x = C ) }

Syntax hints:   \/ w3o 1036   = wceq 1483   {cab 2608   {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:  tprot  4284  tpid3gOLD  4306  en3lplem2  8512  tpid3gVD  39077  en3lplem2VD  39079