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Mirrors > Home > ILE Home > Th. List > prssi | Unicode version |
Description: A pair of elements of a class is a subset of the class. (Contributed by NM, 16-Jan-2015.) |
Ref | Expression |
---|---|
prssi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prssg 3713 | . 2 | |
2 | 1 | ibi 175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 2128 wss 3102 cpr 3561 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3566 df-pr 3567 |
This theorem is referenced by: tpssi 3722 prelpwi 4174 onun2 4449 onintexmid 4532 nnregexmid 4580 en2eqpr 6852 m1expcl2 10441 m1expcl 10442 minmax 11129 xrminmax 11162 1idssfct 11991 unopn 12403 bdop 13450 012of 13567 isomninnlem 13601 trilpolemisumle 13609 trilpolemeq1 13611 trilpolemlt1 13612 iswomninnlem 13620 iswomni0 13622 ismkvnnlem 13623 nconstwlpolemgt0 13634 |
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