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Mirrors > Home > ILE Home > Th. List > prsstp23 | GIF version |
Description: A pair is a subset of an unordered triple containing its members. (Contributed by Jim Kingdon, 11-Aug-2018.) |
Ref | Expression |
---|---|
prsstp23 | ⊢ {𝐵, 𝐶} ⊆ {𝐴, 𝐵, 𝐶} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prsstp12 3590 | . 2 ⊢ {𝐵, 𝐶} ⊆ {𝐵, 𝐶, 𝐴} | |
2 | tprot 3535 | . 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴} | |
3 | 1, 2 | sseqtr4i 3059 | 1 ⊢ {𝐵, 𝐶} ⊆ {𝐴, 𝐵, 𝐶} |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 2999 {cpr 3447 {ctp 3448 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3or 925 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-sn 3452 df-pr 3453 df-tp 3454 |
This theorem is referenced by: sstpr 3601 |
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