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Theorem dftp2 4366
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 = 𝐴𝑥 = 𝐵𝑥 = 𝐶)}
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵   𝑥,𝐶

Proof of Theorem dftp2
StepHypRef Expression
1 vex 3352 . . 3 𝑥 ∈ V
21eltp 4365 . 2 (𝑥 ∈ {𝐴, 𝐵, 𝐶} ↔ (𝑥 = 𝐴𝑥 = 𝐵𝑥 = 𝐶))
32abbi2i 2886 1 {𝐴, 𝐵, 𝐶} = {𝑥 ∣ (𝑥 = 𝐴𝑥 = 𝐵𝑥 = 𝐶)}
Colors of variables: wff setvar class
Syntax hints:  w3o 1069   = wceq 1630  {cab 2756  {ctp 4318
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3or 1071  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-v 3351  df-un 3726  df-sn 4315  df-pr 4317  df-tp 4319
This theorem is referenced by:  tprot  4418  en3lplem2  8671  tpid3gVD  39593  en3lplem2VD  39595
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