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Mirrors > Home > ILE Home > Th. List > riotass2 | Unicode version |
Description: Restriction of a unique element to a smaller class. (Contributed by NM, 21-Aug-2011.) (Revised by NM, 22-Mar-2013.) |
Ref | Expression |
---|---|
riotass2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reuss2 3326 | . . . 4 | |
2 | simplr 504 | . . . 4 | |
3 | riotasbc 5713 | . . . . 5 | |
4 | riotacl 5712 | . . . . . 6 | |
5 | rspsbc 2963 | . . . . . . 7 | |
6 | sbcimg 2922 | . . . . . . 7 | |
7 | 5, 6 | sylibd 148 | . . . . . 6 |
8 | 4, 7 | syl 14 | . . . . 5 |
9 | 3, 8 | mpid 42 | . . . 4 |
10 | 1, 2, 9 | sylc 62 | . . 3 |
11 | 1, 4 | syl 14 | . . . . 5 |
12 | ssel 3061 | . . . . . 6 | |
13 | 12 | ad2antrr 479 | . . . . 5 |
14 | 11, 13 | mpd 13 | . . . 4 |
15 | simprr 506 | . . . 4 | |
16 | nfriota1 5705 | . . . . 5 | |
17 | 16 | nfsbc1 2899 | . . . . 5 |
18 | sbceq1a 2891 | . . . . 5 | |
19 | 16, 17, 18 | riota2f 5719 | . . . 4 |
20 | 14, 15, 19 | syl2anc 408 | . . 3 |
21 | 10, 20 | mpbid 146 | . 2 |
22 | 21 | eqcomd 2123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wcel 1465 wral 2393 wrex 2394 wreu 2395 wsbc 2882 wss 3041 crio 5697 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-uni 3707 df-iota 5058 df-riota 5698 |
This theorem is referenced by: (None) |
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