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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 3677 | . 2 | |
2 | 1 | ibi 175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1480 wss 3071 cpr 3528 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 |
This theorem is referenced by: tpssi 3686 prelpwi 4136 onun2 4406 onintexmid 4487 nnregexmid 4534 en2eqpr 6801 m1expcl2 10315 m1expcl 10316 minmax 11001 xrminmax 11034 1idssfct 11796 unopn 12172 bdop 13073 isomninnlem 13225 trilpolemisumle 13231 trilpolemeq1 13233 trilpolemlt1 13234 |
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