Theorem dftp2 1835

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 group(s):   x,A   x,B   x,C

Proof of Theorem dftp2

Step	Hyp	Ref	Expression
1		visset 1350	. . 3 ⊢ x ∈ V
2	1	eltp 1834	. 2 ⊢ (x ∈ {A, B, C} ↔ (x = A ∨ x = B ∨ x = C))
3	2	biabri 1180	1 ⊢ {A, B, C} = {x∣(x = A ∨ x = B ∨ x = C)}

Syntax hints:   ∨ w3o 580  {cab 1090   = wceq 1091  {ctp 1813

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-3or 582  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490  df-sn 1811  df-pr 1812  df-tp 1814

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