Theorem prsstp13 3669

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 3668	. 2 ⊢ {𝐴, 𝐶} ⊆ {𝐴, 𝐶, 𝐵}
2		tpcomb 3613	. 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}
3	1, 2	sseqtrri 3127	1 ⊢ {𝐴, 𝐶} ⊆ {𝐴, 𝐵, 𝐶}

Syntax hints:   ⊆ wss 3066  {cpr 3523  {ctp 3524

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 2119

This theorem depends on definitions:  df-bi 116  df-3or 963  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-sn 3528  df-pr 3529  df-tp 3530

This theorem is referenced by:  sstpr  3679