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Theorem prsstp13 3674
Description: A pair is a subset of an unordered triple containing its members. (Contributed by Jim Kingdon, 11-Aug-2018.)
Assertion
Ref Expression
prsstp13 {𝐴, 𝐶} ⊆ {𝐴, 𝐵, 𝐶}

Proof of Theorem prsstp13
StepHypRef Expression
1 prsstp12 3673 . 2 {𝐴, 𝐶} ⊆ {𝐴, 𝐶, 𝐵}
2 tpcomb 3618 . 2 {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}
31, 2sseqtrri 3132 1 {𝐴, 𝐶} ⊆ {𝐴, 𝐵, 𝐶}
Colors of variables: wff set class
Syntax hints:  wss 3071  {cpr 3528  {ctp 3529
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-3or 963  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-sn 3533  df-pr 3534  df-tp 3535
This theorem is referenced by:  sstpr  3684
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