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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 1967 |
. . . . . 6
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3 | ancom 253 |
. . . . . . 7
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4 | 3 | mobii 1934 |
. . . . . 6
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5 | 2, 4 | mpbi 133 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 5 | ax-gen 1335 |
. . . 4
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7 | excom 1551 |
. . . . . 6
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8 | 7 | dcbii 746 |
. . . . 5
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9 | 2euswapdc 1988 |
. . . . 5
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10 | 8, 9 | sylbi 114 |
. . . 4
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11 | 6, 10 | mpi 15 |
. . 3
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12 | moeq 2710 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() | |
13 | 12 | moani 1967 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 3 | mobii 1934 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 13, 14 | mpbi 133 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15 | ax-gen 1335 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 2euswapdc 1988 |
. . . 4
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18 | 16, 17 | mpi 15 |
. . 3
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19 | 11, 18 | impbid 120 |
. 2
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20 | euxfr2dc.1 |
. . . 4
![]() ![]() ![]() ![]() | |
21 | biidd 161 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | 20, 21 | ceqsexv 2587 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 22 | eubii 1906 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 19, 23 | syl6bb 185 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-dc 742 df-tru 1245 df-nf 1347 df-sb 1643 df-eu 1900 df-mo 1901 df-clab 2024 df-cleq 2030 df-clel 2033 df-v 2553 |
This theorem is referenced by: euxfrdc 2721 |
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