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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 2700 |
. 2
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2 | vtocl2gf.3 |
. . 3
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3 | vtocl2gf.2 |
. . . . 5
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4 | 3 | nfel1 2293 |
. . . 4
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5 | vtocl2gf.5 |
. . . 4
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6 | 4, 5 | nfim 1552 |
. . 3
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7 | vtocl2gf.7 |
. . . 4
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8 | 7 | imbi2d 229 |
. . 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 2747 |
. . 3
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14 | 2, 6, 8, 13 | vtoclgf 2747 |
. 2
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15 | 1, 14 | mpan9 279 |
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-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 |
This theorem is referenced by: vtocl3gf 2752 vtocl2g 2753 vtocl2gaf 2756 |
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