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Mirrors > Home > ILE Home > Th. List > euxfr2dc | Unicode version |
Description: Transfer existential
uniqueness from a variable ![]() ![]() ![]() |
Ref | Expression |
---|---|
euxfr2dc.1 |
![]() ![]() ![]() ![]() |
euxfr2dc.2 |
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Ref | Expression |
---|---|
euxfr2dc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euxfr2dc.2 |
. . . . . . 7
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2 | 1 | moani 2106 |
. . . . . 6
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3 | ancom 266 |
. . . . . . 7
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4 | 3 | mobii 2073 |
. . . . . 6
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5 | 2, 4 | mpbi 145 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 5 | ax-gen 1459 |
. . . 4
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7 | excom 1674 |
. . . . . 6
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8 | 7 | dcbii 841 |
. . . . 5
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9 | 2euswapdc 2127 |
. . . . 5
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10 | 8, 9 | sylbi 121 |
. . . 4
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11 | 6, 10 | mpi 15 |
. . 3
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12 | moeq 2924 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() | |
13 | 12 | moani 2106 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 3 | mobii 2073 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 13, 14 | mpbi 145 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15 | ax-gen 1459 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 2euswapdc 2127 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 16, 17 | mpi 15 |
. . 3
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19 | 11, 18 | impbid 129 |
. 2
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20 | euxfr2dc.1 |
. . . 4
![]() ![]() ![]() ![]() | |
21 | biidd 172 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | 20, 21 | ceqsexv 2788 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 22 | eubii 2045 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 19, 23 | bitrdi 196 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-in1 615 ax-in2 616 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-dc 836 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-v 2751 |
This theorem is referenced by: euxfrdc 2935 |
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