Theorem prsstp23 3641

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}

Proof of Theorem prsstp23

Step	Hyp	Ref	Expression
1		prsstp12 3639	. 2 ⊢ {𝐵, 𝐶} ⊆ {𝐵, 𝐶, 𝐴}
2		tprot 3582	. 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3	1, 2	sseqtr4i 3098	1 ⊢ {𝐵, 𝐶} ⊆ {𝐴, 𝐵, 𝐶}

Syntax hints:   ⊆ wss 3037  {cpr 3494  {ctp 3495

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097

This theorem depends on definitions:  df-bi 116  df-3or 946  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2244  df-v 2659  df-un 3041  df-in 3043  df-ss 3050  df-sn 3499  df-pr 3500  df-tp 3501

This theorem is referenced by:  sstpr  3650