Theorem dftp2 3671

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 2766	. . 3 |- x e. _V
2	1	eltp 3670	. 2 |- ( x e. { A , B , C } <-> ( x = A \/ x = B \/ x = C ) )
3	2	abbi2i 2311	1 |- { A , B , C } = { x | ( x = A \/ x = B \/ x = C ) }

Syntax hints:   \/ w3o 979   = wceq 1364   {cab 2182   {ctp 3624

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-3or 981  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-un 3161  df-sn 3628  df-pr 3629  df-tp 3630

This theorem is referenced by:  tprot  3715  tpid3g  3737