Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  prsstp23 GIF version

 Description: A pair is a subset of an unordered triple containing its members. (Contributed by Jim Kingdon, 11-Aug-2018.)
Assertion
Ref Expression
prsstp23 {𝐵, 𝐶} ⊆ {𝐴, 𝐵, 𝐶}

StepHypRef Expression
1 prsstp12 3545 . 2 {𝐵, 𝐶} ⊆ {𝐵, 𝐶, 𝐴}
2 tprot 3491 . 2 {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
31, 2sseqtr4i 3006 1 {𝐵, 𝐶} ⊆ {𝐴, 𝐵, 𝐶}
 Colors of variables: wff set class Syntax hints:   ⊆ wss 2945  {cpr 3404  {ctp 3405 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3or 897  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-sn 3409  df-pr 3410  df-tp 3411 This theorem is referenced by:  sstpr  3556
 Copyright terms: Public domain W3C validator