Theorem prsstp23 3788

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 3786	. 2 ⊢ {𝐵, 𝐶} ⊆ {𝐵, 𝐶, 𝐴}
2		tprot 3726	. 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3	1, 2	sseqtrri 3228	1 ⊢ {𝐵, 𝐶} ⊆ {𝐴, 𝐵, 𝐶}

Syntax hints:   ⊆ wss 3166  {cpr 3634  {ctp 3635

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3or 982  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-un 3170  df-in 3172  df-ss 3179  df-sn 3639  df-pr 3640  df-tp 3641

This theorem is referenced by:  sstpr  3798