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Theorem tprot 3815
 Description: Rotation of the elements of an unordered triple. (Contributed by Alan Sare, 24-Oct-2011.)
Assertion
Ref Expression
tprot {A, B, C} = {B, C, A}

Proof of Theorem tprot
Dummy variable x is distinct from all other variables.
StepHypRef Expression
1 3orrot 940 . . 3 ((x = A x = B x = C) ↔ (x = B x = C x = A))
21abbii 2465 . 2 {x (x = A x = B x = C)} = {x (x = B x = C x = A)}
3 dftp2 3772 . 2 {A, B, C} = {x (x = A x = B x = C)}
4 dftp2 3772 . 2 {B, C, A} = {x (x = B x = C x = A)}
52, 3, 43eqtr4i 2383 1 {A, B, C} = {B, C, A}
 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:  tpcomb  3817  tpass  3818  tpidm13  3822  tpidm23  3823
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