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Theorem tpcomb 3465
 Description: Swap 2nd and 3rd members of an undordered triple. (Contributed by NM, 22-May-2015.)
Assertion
Ref Expression
tpcomb {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Proof of Theorem tpcomb
StepHypRef Expression
1 tpcoma 3464 . 2 {𝐵, 𝐶, 𝐴} = {𝐶, 𝐵, 𝐴}
2 tprot 3463 . 2 {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3 tprot 3463 . 2 {𝐴, 𝐶, 𝐵} = {𝐶, 𝐵, 𝐴}
41, 2, 33eqtr4i 2070 1 {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}
 Colors of variables: wff set class Syntax hints:   = wceq 1243  {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-3or 886  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-sn 3381  df-pr 3382  df-tp 3383 This theorem is referenced by:  prsstp13  3518
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