Theorem prsstp13 3559

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

Step	Hyp	Ref	Expression
1		prsstp12 3558	. 2 ⊢ {𝐴, 𝐶} ⊆ {𝐴, 𝐶, 𝐵}
2		tpcomb 3505	. 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}
3	1, 2	sseqtr4i 3041	1 ⊢ {𝐴, 𝐶} ⊆ {𝐴, 𝐵, 𝐶}

Syntax hints:   ⊆ wss 2982  {cpr 3417  {ctp 3418

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-3or 921  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-sn 3422  df-pr 3423  df-tp 3424

This theorem is referenced by:  sstpr  3569