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Mirrors > Home > MPE Home > Th. List > vtocl2gaf | Structured version Visualization version 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 2608 |
. . . . 5
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5 | nfv 1763 |
. . . . 5
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6 | 4, 5 | nfan 2013 |
. . . 4
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7 | vtocl2gaf.1 |
. . . 4
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8 | 6, 7 | nfim 2005 |
. . 3
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9 | 2 | nfel1 2608 |
. . . . 5
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10 | 3 | nfel1 2608 |
. . . . 5
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11 | 9, 10 | nfan 2013 |
. . . 4
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12 | vtocl2gaf.2 |
. . . 4
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13 | 11, 12 | nfim 2005 |
. . 3
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14 | eleq1 2519 |
. . . . 5
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15 | 14 | anbi1d 712 |
. . . 4
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16 | vtocl2gaf.3 |
. . . 4
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17 | 15, 16 | imbi12d 322 |
. . 3
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18 | eleq1 2519 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 18 | anbi2d 711 |
. . . 4
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20 | vtocl2gaf.4 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 19, 20 | imbi12d 322 |
. . 3
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22 | vtocl2gaf.5 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 1, 2, 3, 8, 13, 17, 21, 22 | vtocl2gf 3111 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 23 | pm2.43i 49 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-v 3049 |
This theorem is referenced by: vtocl2ga 3117 ovmpt2s 6425 ov2gf 6426 ov3 6438 pwfseqlem2 9089 cnmptcom 20705 |
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