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Mirrors > Home > NFE Home > Th. List > vtocl2gaf | Unicode version |
Description: Implicit substitution of 2 classes for 2 setvar variables. (Contributed by NM, 10-Aug-2013.) |
Ref | Expression |
---|---|
vtocl2gaf.a |
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vtocl2gaf.b |
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vtocl2gaf.c |
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vtocl2gaf.1 |
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vtocl2gaf.2 |
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vtocl2gaf.3 |
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vtocl2gaf.4 |
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vtocl2gaf.5 |
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Ref | Expression |
---|---|
vtocl2gaf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocl2gaf.a |
. . 3
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2 | vtocl2gaf.b |
. . 3
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3 | vtocl2gaf.c |
. . 3
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4 | 1 | nfel1 2500 |
. . . . 5
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5 | nfv 1619 |
. . . . 5
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6 | 4, 5 | nfan 1824 |
. . . 4
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7 | vtocl2gaf.1 |
. . . 4
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8 | 6, 7 | nfim 1813 |
. . 3
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9 | 2 | nfel1 2500 |
. . . . 5
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10 | 3 | nfel1 2500 |
. . . . 5
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11 | 9, 10 | nfan 1824 |
. . . 4
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12 | vtocl2gaf.2 |
. . . 4
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13 | 11, 12 | nfim 1813 |
. . 3
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14 | eleq1 2413 |
. . . . 5
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15 | 14 | anbi1d 685 |
. . . 4
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16 | vtocl2gaf.3 |
. . . 4
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17 | 15, 16 | imbi12d 311 |
. . 3
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18 | eleq1 2413 |
. . . . 5
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19 | 18 | anbi2d 684 |
. . . 4
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20 | vtocl2gaf.4 |
. . . 4
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21 | 19, 20 | imbi12d 311 |
. . 3
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22 | vtocl2gaf.5 |
. . 3
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23 | 1, 2, 3, 8, 13, 17, 21, 22 | vtocl2gf 2917 |
. 2
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24 | 23 | pm2.43i 43 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-v 2862 |
This theorem is referenced by: vtocl2ga 2923 ov3 5600 ov2gf 5712 |
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