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Theorem prsstp13 3734
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 }  C_  { A ,  B ,  C }

Proof of Theorem prsstp13
StepHypRef Expression
1 prsstp12 3733 . 2  |-  { A ,  C }  C_  { A ,  C ,  B }
2 tpcomb 3678 . 2  |-  { A ,  B ,  C }  =  { A ,  C ,  B }
31, 2sseqtrri 3182 1  |-  { A ,  C }  C_  { A ,  B ,  C }
Colors of variables: wff set class
Syntax hints:    C_ wss 3121   {cpr 3584   {ctp 3585
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-3or 974  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-sn 3589  df-pr 3590  df-tp 3591
This theorem is referenced by:  sstpr  3744
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