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Mirrors > Home > ILE Home > Th. List > riota2df | Unicode version |
Description: A deduction version of riota2f 5759. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
riota2df.1 |
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riota2df.2 |
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riota2df.3 |
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riota2df.4 |
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riota2df.5 |
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Ref | Expression |
---|---|
riota2df |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | riota2df.4 |
. . . 4
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2 | 1 | adantr 274 |
. . 3
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3 | simpr 109 |
. . . 4
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4 | df-reu 2424 |
. . . 4
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5 | 3, 4 | sylib 121 |
. . 3
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6 | simpr 109 |
. . . . . 6
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7 | 2 | adantr 274 |
. . . . . 6
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8 | 6, 7 | eqeltrd 2217 |
. . . . 5
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9 | 8 | biantrurd 303 |
. . . 4
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10 | riota2df.5 |
. . . . 5
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11 | 10 | adantlr 469 |
. . . 4
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12 | 9, 11 | bitr3d 189 |
. . 3
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13 | riota2df.1 |
. . . 4
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14 | nfreu1 2605 |
. . . 4
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15 | 13, 14 | nfan 1545 |
. . 3
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16 | riota2df.3 |
. . . 4
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17 | 16 | adantr 274 |
. . 3
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18 | riota2df.2 |
. . . 4
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19 | 18 | adantr 274 |
. . 3
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20 | 2, 5, 12, 15, 17, 19 | iota2df 5120 |
. 2
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21 | df-riota 5738 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | 21 | eqeq1i 2148 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 20, 22 | syl6bbr 197 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-reu 2424 df-v 2691 df-sbc 2914 df-un 3080 df-sn 3538 df-pr 3539 df-uni 3745 df-iota 5096 df-riota 5738 |
This theorem is referenced by: riota2f 5759 riota5f 5762 |
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