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Mirrors > Home > ILE Home > Th. List > iotass | Unicode version |
Description: Value of iota based on a proposition which holds only for values which are subsets of a given class. (Contributed by Mario Carneiro and Jim Kingdon, 21-Dec-2018.) |
Ref | Expression |
---|---|
iotass |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iota 5096 |
. 2
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2 | unieq 3753 |
. . . . . . . 8
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3 | vex 2692 |
. . . . . . . . 9
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4 | 3 | unisn 3760 |
. . . . . . . 8
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5 | 2, 4 | eqtrdi 2189 |
. . . . . . 7
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6 | df-pw 3517 |
. . . . . . . . . . 11
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7 | 6 | sseq2i 3129 |
. . . . . . . . . 10
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8 | ss2ab 3170 |
. . . . . . . . . 10
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9 | 7, 8 | bitri 183 |
. . . . . . . . 9
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10 | 9 | biimpri 132 |
. . . . . . . 8
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11 | sspwuni 3905 |
. . . . . . . 8
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12 | 10, 11 | sylib 121 |
. . . . . . 7
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13 | sseq1 3125 |
. . . . . . . 8
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14 | 13 | biimpa 294 |
. . . . . . 7
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15 | 5, 12, 14 | syl2anr 288 |
. . . . . 6
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16 | 15 | ex 114 |
. . . . 5
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17 | 16 | ss2abdv 3175 |
. . . 4
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18 | df-pw 3517 |
. . . 4
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19 | 17, 18 | sseqtrrdi 3151 |
. . 3
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20 | sspwuni 3905 |
. . 3
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21 | 19, 20 | sylib 121 |
. 2
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22 | 1, 21 | eqsstrid 3148 |
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-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-uni 3745 df-iota 5096 |
This theorem is referenced by: fvss 5443 riotaexg 5742 |
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