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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 3430 |
. . . 4
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2 | simplr 528 |
. . . 4
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3 | riotasbc 5862 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | riotacl 5861 |
. . . . . 6
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5 | rspsbc 3060 |
. . . . . . 7
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6 | sbcimg 3019 |
. . . . . . 7
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7 | 5, 6 | sylibd 149 |
. . . . . 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 3164 |
. . . . . 6
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13 | 12 | ad2antrr 488 |
. . . . 5
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14 | 11, 13 | mpd 13 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | simprr 531 |
. . . 4
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16 | nfriota1 5854 |
. . . . 5
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17 | 16 | nfsbc1 2995 |
. . . . 5
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18 | sbceq1a 2987 |
. . . . 5
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19 | 16, 17, 18 | riota2f 5868 |
. . . 4
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20 | 14, 15, 19 | syl2anc 411 |
. . 3
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21 | 10, 20 | mpbid 147 |
. 2
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22 | 21 | eqcomd 2195 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-uni 3825 df-iota 5193 df-riota 5847 |
This theorem is referenced by: (None) |
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