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Mirrors > Home > ILE Home > Th. List > moriotass | Unicode version |
Description: Restriction of a unique element to a smaller class. (Contributed by NM, 19-Feb-2006.) (Revised by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
moriotass |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrexv 3005 | . . . . 5 | |
2 | 1 | imp 115 | . . . 4 |
3 | 2 | 3adant3 924 | . . 3 |
4 | simp3 906 | . . 3 | |
5 | reu5 2522 | . . 3 | |
6 | 3, 4, 5 | sylanbrc 394 | . 2 |
7 | riotass 5495 | . 2 | |
8 | 6, 7 | syld3an3 1180 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3a 885 wceq 1243 wrex 2307 wreu 2308 wrmo 2309 wss 2917 crio 5467 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-reu 2313 df-rmo 2314 df-rab 2315 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-uni 3581 df-iota 4867 df-riota 5468 |
This theorem is referenced by: (None) |
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