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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 3322 |
. . . 4
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2 | simplr 502 |
. . . 4
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3 | riotasbc 5699 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | riotacl 5698 |
. . . . . 6
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5 | rspsbc 2959 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | sbcimg 2918 |
. . . . . . 7
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7 | 5, 6 | sylibd 148 |
. . . . . 6
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8 | 4, 7 | syl 14 |
. . . . 5
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9 | 3, 8 | mpid 42 |
. . . 4
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10 | 1, 2, 9 | sylc 62 |
. . 3
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11 | 1, 4 | syl 14 |
. . . . 5
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12 | ssel 3057 |
. . . . . 6
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13 | 12 | ad2antrr 477 |
. . . . 5
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14 | 11, 13 | mpd 13 |
. . . 4
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15 | simprr 504 |
. . . 4
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16 | nfriota1 5691 |
. . . . 5
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17 | 16 | nfsbc1 2895 |
. . . . 5
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18 | sbceq1a 2887 |
. . . . 5
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19 | 16, 17, 18 | riota2f 5705 |
. . . 4
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20 | 14, 15, 19 | syl2anc 406 |
. . 3
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21 | 10, 20 | mpbid 146 |
. 2
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22 | 21 | eqcomd 2120 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-ral 2395 df-rex 2396 df-reu 2397 df-rab 2399 df-v 2659 df-sbc 2879 df-un 3041 df-in 3043 df-ss 3050 df-sn 3499 df-pr 3500 df-uni 3703 df-iota 5046 df-riota 5684 |
This theorem is referenced by: (None) |
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