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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 3427 |
. . . 4
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2 | simplr 528 |
. . . 4
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3 | riotasbc 5859 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | riotacl 5858 |
. . . . . 6
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5 | rspsbc 3057 |
. . . . . . 7
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6 | sbcimg 3016 |
. . . . . . 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 3161 |
. . . . . 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 5851 |
. . . . 5
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17 | 16 | nfsbc1 2992 |
. . . . 5
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18 | sbceq1a 2984 |
. . . . 5
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19 | 16, 17, 18 | riota2f 5865 |
. . . 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 2193 |
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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-reu 2472 df-rab 2474 df-v 2751 df-sbc 2975 df-un 3145 df-in 3147 df-ss 3154 df-sn 3610 df-pr 3611 df-uni 3822 df-iota 5190 df-riota 5844 |
This theorem is referenced by: (None) |
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