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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 3356 | . . . 4 | |
2 | simplr 519 | . . . 4 | |
3 | riotasbc 5745 | . . . . 5 | |
4 | riotacl 5744 | . . . . . 6 | |
5 | rspsbc 2991 | . . . . . . 7 | |
6 | sbcimg 2950 | . . . . . . 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 3091 | . . . . . 6 | |
13 | 12 | ad2antrr 479 | . . . . 5 |
14 | 11, 13 | mpd 13 | . . . 4 |
15 | simprr 521 | . . . 4 | |
16 | nfriota1 5737 | . . . . 5 | |
17 | 16 | nfsbc1 2926 | . . . . 5 |
18 | sbceq1a 2918 | . . . . 5 | |
19 | 16, 17, 18 | riota2f 5751 | . . . 4 |
20 | 14, 15, 19 | syl2anc 408 | . . 3 |
21 | 10, 20 | mpbid 146 | . 2 |
22 | 21 | eqcomd 2145 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wral 2416 wrex 2417 wreu 2418 wsbc 2909 wss 3071 crio 5729 |
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-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-uni 3737 df-iota 5088 df-riota 5730 |
This theorem is referenced by: (None) |
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