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Theorem dftp2 3772
 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
StepHypRef Expression
1 vex 2862 . . 3 x V
21eltp 3771 . 2 (x {A, B, C} ↔ (x = A x = B x = C))
32abbi2i 2464 1 {A, B, C} = {x (x = A x = B x = C)}
 Colors of variables: wff setvar class Syntax hints:   ∨ w3o 933   = wceq 1642  {cab 2339  {ctp 3739 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742  df-tp 3743 This theorem is referenced by:  tprot  3815  tpid3g  3831
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