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Mirrors > Home > ILE Home > Th. List > spc2ed | Unicode version |
Description: Existential specialization with 2 quantifiers, using implicit substitution. (Contributed by Thierry Arnoux, 23-Aug-2017.) |
Ref | Expression |
---|---|
spc2ed.x |
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spc2ed.y |
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spc2ed.1 |
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Ref | Expression |
---|---|
spc2ed |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2703 |
. . . 4
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2 | elisset 2703 |
. . . 4
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3 | 1, 2 | anim12i 336 |
. . 3
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4 | eeanv 1905 |
. . 3
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5 | 3, 4 | sylibr 133 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | nfv 1509 |
. . . . 5
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7 | spc2ed.x |
. . . . 5
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8 | 6, 7 | nfan 1545 |
. . . 4
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9 | nfv 1509 |
. . . . . 6
![]() ![]() ![]() ![]() | |
10 | spc2ed.y |
. . . . . 6
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11 | 9, 10 | nfan 1545 |
. . . . 5
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12 | anass 399 |
. . . . . . . 8
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13 | ancom 264 |
. . . . . . . . 9
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14 | 13 | anbi1i 454 |
. . . . . . . 8
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15 | 12, 14 | bitr3i 185 |
. . . . . . 7
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16 | spc2ed.1 |
. . . . . . . 8
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17 | 16 | biimparc 297 |
. . . . . . 7
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18 | 15, 17 | sylbir 134 |
. . . . . 6
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19 | 18 | ex 114 |
. . . . 5
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20 | 11, 19 | eximd 1592 |
. . . 4
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21 | 8, 20 | eximd 1592 |
. . 3
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22 | 21 | impancom 258 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 5, 22 | sylan2 284 |
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-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-v 2691 |
This theorem is referenced by: cnvoprab 6139 |
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