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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 3397 | . . . 4 | |
2 | simplr 520 | . . . 4 | |
3 | riotasbc 5807 | . . . . 5 | |
4 | riotacl 5806 | . . . . . 6 | |
5 | rspsbc 3028 | . . . . . . 7 | |
6 | sbcimg 2987 | . . . . . . 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 3131 | . . . . . 6 | |
13 | 12 | ad2antrr 480 | . . . . 5 |
14 | 11, 13 | mpd 13 | . . . 4 |
15 | simprr 522 | . . . 4 | |
16 | nfriota1 5799 | . . . . 5 | |
17 | 16 | nfsbc1 2963 | . . . . 5 |
18 | sbceq1a 2955 | . . . . 5 | |
19 | 16, 17, 18 | riota2f 5813 | . . . 4 |
20 | 14, 15, 19 | syl2anc 409 | . . 3 |
21 | 10, 20 | mpbid 146 | . 2 |
22 | 21 | eqcomd 2170 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wcel 2135 wral 2442 wrex 2443 wreu 2444 wsbc 2946 wss 3111 crio 5791 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-reu 2449 df-rab 2451 df-v 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-sn 3576 df-pr 3577 df-uni 3784 df-iota 5147 df-riota 5792 |
This theorem is referenced by: (None) |
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