Theorem prsstp23 3794

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 3792	. 2 ⊢ {𝐵, 𝐶} ⊆ {𝐵, 𝐶, 𝐴}
2		tprot 3731	. 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3	1, 2	sseqtrri 3232	1 ⊢ {𝐵, 𝐶} ⊆ {𝐴, 𝐵, 𝐶}

Syntax hints:   ⊆ wss 3170  {cpr 3639  {ctp 3640

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-3or 982  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-v 2775  df-un 3174  df-in 3176  df-ss 3183  df-sn 3644  df-pr 3645  df-tp 3646

This theorem is referenced by:  sstpr  3806