Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 3685 | . 2 | |
2 | 1 | ibi 175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1481 wss 3076 cpr 3533 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 |
This theorem is referenced by: tpssi 3694 prelpwi 4144 onun2 4414 onintexmid 4495 nnregexmid 4542 en2eqpr 6809 m1expcl2 10346 m1expcl 10347 minmax 11033 xrminmax 11066 1idssfct 11832 unopn 12211 bdop 13244 012of 13363 isomninnlem 13400 trilpolemisumle 13406 trilpolemeq1 13408 trilpolemlt1 13409 iswomninnlem 13417 ismkvnnlem 13419 |
Copyright terms: Public domain | W3C validator |