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Theorem tpcoma 3816
 Description: Swap 1st and 2nd members of an undordered triple. (Contributed by NM, 22-May-2015.)
Assertion
Ref Expression
tpcoma {A, B, C} = {B, A, C}

Proof of Theorem tpcoma
StepHypRef Expression
1 prcom 3798 . . 3 {A, B} = {B, A}
21uneq1i 3414 . 2 ({A, B} ∪ {C}) = ({B, A} ∪ {C})
3 df-tp 3743 . 2 {A, B, C} = ({A, B} ∪ {C})
4 df-tp 3743 . 2 {B, A, C} = ({B, A} ∪ {C})
52, 3, 43eqtr4i 2383 1 {A, B, C} = {B, A, C}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∪ cun 3207  {csn 3737  {cpr 3738  {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-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-pr 3742  df-tp 3743 This theorem is referenced by:  tpcomb  3817
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