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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 3211 |
. . . 4
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2 | simplr 482 |
. . . 4
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3 | riotasbc 5426 |
. . . . 5
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4 | riotacl 5425 |
. . . . . 6
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5 | rspsbc 2834 |
. . . . . . 7
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6 | sbcimg 2798 |
. . . . . . 7
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7 | 5, 6 | sylibd 138 |
. . . . . 6
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8 | 4, 7 | syl 14 |
. . . . 5
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9 | 3, 8 | mpid 37 |
. . . 4
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10 | 1, 2, 9 | sylc 56 |
. . 3
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11 | 1, 4 | syl 14 |
. . . . 5
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12 | ssel 2933 |
. . . . . 6
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13 | 12 | ad2antrr 457 |
. . . . 5
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14 | 11, 13 | mpd 13 |
. . . 4
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15 | simprr 484 |
. . . 4
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16 | nfriota1 5418 |
. . . . 5
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17 | 16 | nfsbc1 2775 |
. . . . 5
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18 | sbceq1a 2767 |
. . . . 5
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19 | 16, 17, 18 | riota2f 5432 |
. . . 4
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20 | 14, 15, 19 | syl2anc 391 |
. . 3
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21 | 10, 20 | mpbid 135 |
. 2
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22 | 21 | eqcomd 2042 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-reu 2307 df-rab 2309 df-v 2553 df-sbc 2759 df-un 2916 df-in 2918 df-ss 2925 df-sn 3373 df-pr 3374 df-uni 3572 df-iota 4810 df-riota 5411 |
This theorem is referenced by: (None) |
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