Theorem dftp2 2440

Description: Alternate definition of unordered triple of classes. Special case of Definition 5.3 of [TakeutiZaring] p. 16.

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		visset 1813	. . 3 |- x e. V
2	1	eltp 2439	. 2 |- (x e. {A, B, C} <-> (x = A \/ x = B \/ x = C))
3	2	abbi2i 1574	1 |- {A, B, C} = {x | (x = A \/ x = B \/ x = C)}

Syntax hints:   \/ w3o 774   = wceq 956  {cab 1463  {ctp 2414

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-3or 776  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050  df-sn 2412  df-pr 2413  df-tp 2415

Copyright terms: Public domain