Theorem dftp2 2444

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 1816	. . 3 |- x e. V
2	1	eltp 2443	. 2 |- (x e. {A, B, C} <-> (x = A \/ x = B \/ x = C))
3	2	abbi2i 1577	1 |- {A, B, C} = {x | (x = A \/ x = B \/ x = C)}

Syntax hints:   \/ w3o 776   = wceq 958  {cab 1466  {ctp 2418

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-3or 778  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-un 2053  df-sn 2416  df-pr 2417  df-tp 2419

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