Theorem prsstp13 3758

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 3757	. 2 ⊢ {𝐴, 𝐶} ⊆ {𝐴, 𝐶, 𝐵}
2		tpcomb 3699	. 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}
3	1, 2	sseqtrri 3202	1 ⊢ {𝐴, 𝐶} ⊆ {𝐴, 𝐵, 𝐶}

Syntax hints:   ⊆ wss 3141  {cpr 3605  {ctp 3606

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 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-3or 980  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-un 3145  df-in 3147  df-ss 3154  df-sn 3610  df-pr 3611  df-tp 3612

This theorem is referenced by:  sstpr  3769