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Mirrors > Home > ILE Home > Th. List > vtocl2gf | Unicode version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 25-Apr-1995.) |
Ref | Expression |
---|---|
vtocl2gf.1 |
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vtocl2gf.2 |
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vtocl2gf.3 |
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vtocl2gf.4 |
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vtocl2gf.5 |
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vtocl2gf.6 |
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vtocl2gf.7 |
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vtocl2gf.8 |
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Ref | Expression |
---|---|
vtocl2gf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2748 |
. 2
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2 | vtocl2gf.3 |
. . 3
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3 | vtocl2gf.2 |
. . . . 5
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4 | 3 | nfel1 2330 |
. . . 4
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5 | vtocl2gf.5 |
. . . 4
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6 | 4, 5 | nfim 1572 |
. . 3
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7 | vtocl2gf.7 |
. . . 4
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8 | 7 | imbi2d 230 |
. . 3
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9 | vtocl2gf.1 |
. . . 4
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10 | vtocl2gf.4 |
. . . 4
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11 | vtocl2gf.6 |
. . . 4
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12 | vtocl2gf.8 |
. . . 4
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13 | 9, 10, 11, 12 | vtoclgf 2795 |
. . 3
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14 | 2, 6, 8, 13 | vtoclgf 2795 |
. 2
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15 | 1, 14 | mpan9 281 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 |
This theorem is referenced by: vtocl3gf 2800 vtocl2g 2801 vtocl2gaf 2804 |
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