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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 3737 | . 2 | |
2 | 1 | ibi 175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 2141 wss 3121 cpr 3584 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-pr 3590 |
This theorem is referenced by: tpssi 3746 prelpwi 4199 onun2 4474 onintexmid 4557 nnregexmid 4605 en2eqpr 6885 m1expcl2 10498 m1expcl 10499 minmax 11193 xrminmax 11228 1idssfct 12069 unopn 12797 bdop 13910 012of 14028 isomninnlem 14062 trilpolemisumle 14070 trilpolemeq1 14072 trilpolemlt1 14073 iswomninnlem 14081 iswomni0 14083 ismkvnnlem 14084 nconstwlpolemgt0 14095 |
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