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Mirrors > Home > ILE Home > Th. List > vtoclgf | Unicode version |
Description: Implicit substitution of a class for a setvar variable, with bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.) (Proof shortened by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
vtoclgf.1 |
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vtoclgf.2 |
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vtoclgf.3 |
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vtoclgf.4 |
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Ref | Expression |
---|---|
vtoclgf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2700 |
. 2
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2 | vtoclgf.1 |
. . . 4
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3 | 2 | issetf 2696 |
. . 3
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4 | vtoclgf.2 |
. . . 4
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5 | vtoclgf.4 |
. . . . 5
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6 | vtoclgf.3 |
. . . . 5
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7 | 5, 6 | mpbii 147 |
. . . 4
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8 | 4, 7 | exlimi 1574 |
. . 3
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9 | 3, 8 | sylbi 120 |
. 2
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10 | 1, 9 | syl 14 |
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: vtoclg 2749 vtocl2gf 2751 vtocl3gf 2752 vtoclgaf 2754 ceqsexg 2817 elabgf 2830 mob 2870 opeliunxp2 4687 fvmptss2 5504 |
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