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Theorem tpcoma 3464
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 3446 . . 3  |-  { A ,  B }  =  { B ,  A }
21uneq1i 3093 . 2  |-  ( { A ,  B }  u.  { C } )  =  ( { B ,  A }  u.  { C } )
3 df-tp 3383 . 2  |-  { A ,  B ,  C }  =  ( { A ,  B }  u.  { C } )
4 df-tp 3383 . 2  |-  { B ,  A ,  C }  =  ( { B ,  A }  u.  { C } )
52, 3, 43eqtr4i 2070 1  |-  { A ,  B ,  C }  =  { B ,  A ,  C }
Colors of variables: wff set class
Syntax hints:    = wceq 1243    u. cun 2915   {csn 3375   {cpr 3376   {ctp 3377
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-pr 3382  df-tp 3383
This theorem is referenced by:  tpcomb  3465
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