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Mirrors > Home > ILE Home > Th. List > 2rmorex | Unicode version |
Description: Double restricted quantification with "at most one," analogous to 2moex 2124. (Contributed by Alexander van der Vekens, 17-Jun-2017.) |
Ref | Expression |
---|---|
2rmorex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2474 |
. . . . . . . 8
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2 | 1 | anbi2i 457 |
. . . . . . 7
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3 | 2 | mobii 2075 |
. . . . . 6
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4 | df-rmo 2476 |
. . . . . 6
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5 | 19.42v 1918 |
. . . . . . 7
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6 | 5 | mobii 2075 |
. . . . . 6
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7 | 3, 4, 6 | 3bitr4i 212 |
. . . . 5
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8 | 2moex 2124 |
. . . . 5
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9 | 7, 8 | sylbi 121 |
. . . 4
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10 | an12 561 |
. . . . . 6
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11 | 10 | mobii 2075 |
. . . . 5
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12 | 11 | albii 1481 |
. . . 4
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13 | 9, 12 | sylib 122 |
. . 3
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14 | moanimv 2113 |
. . . 4
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15 | 14 | albii 1481 |
. . 3
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16 | 13, 15 | sylib 122 |
. 2
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17 | df-ral 2473 |
. . 3
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18 | df-rmo 2476 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 18 | imbi2i 226 |
. . . 4
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20 | 19 | albii 1481 |
. . 3
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21 | 17, 20 | bitri 184 |
. 2
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22 | 16, 21 | sylibr 134 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-ral 2473 df-rex 2474 df-rmo 2476 |
This theorem is referenced by: (None) |
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