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Mirrors > Home > ILE Home > Th. List > 2rmorex | Unicode version |
Description: Double restricted quantification with "at most one," analogous to 2moex 2046. (Contributed by Alexander van der Vekens, 17-Jun-2017.) |
Ref | Expression |
---|---|
2rmorex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2381 |
. . . . . . . 8
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2 | 1 | anbi2i 448 |
. . . . . . 7
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3 | 2 | mobii 1997 |
. . . . . 6
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4 | df-rmo 2383 |
. . . . . 6
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5 | 19.42v 1845 |
. . . . . . 7
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6 | 5 | mobii 1997 |
. . . . . 6
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7 | 3, 4, 6 | 3bitr4i 211 |
. . . . 5
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8 | 2moex 2046 |
. . . . 5
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9 | 7, 8 | sylbi 120 |
. . . 4
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10 | an12 531 |
. . . . . 6
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11 | 10 | mobii 1997 |
. . . . 5
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12 | 11 | albii 1414 |
. . . 4
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13 | 9, 12 | sylib 121 |
. . 3
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14 | moanimv 2035 |
. . . 4
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15 | 14 | albii 1414 |
. . 3
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16 | 13, 15 | sylib 121 |
. 2
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17 | df-ral 2380 |
. . 3
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18 | df-rmo 2383 |
. . . . 5
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19 | 18 | imbi2i 225 |
. . . 4
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20 | 19 | albii 1414 |
. . 3
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21 | 17, 20 | bitri 183 |
. 2
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22 | 16, 21 | sylibr 133 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-nf 1405 df-sb 1704 df-eu 1963 df-mo 1964 df-ral 2380 df-rex 2381 df-rmo 2383 |
This theorem is referenced by: (None) |
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