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Mirrors > Home > ILE Home > Th. List > vtocl3gf | Unicode version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 10-Aug-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
vtocl3gf.a |
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vtocl3gf.b |
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vtocl3gf.c |
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vtocl3gf.d |
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vtocl3gf.e |
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vtocl3gf.f |
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vtocl3gf.1 |
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vtocl3gf.2 |
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vtocl3gf.3 |
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vtocl3gf.4 |
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vtocl3gf.5 |
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vtocl3gf.6 |
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vtocl3gf.7 |
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Ref | Expression |
---|---|
vtocl3gf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2700 |
. . 3
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2 | vtocl3gf.d |
. . . 4
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3 | vtocl3gf.e |
. . . 4
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4 | vtocl3gf.f |
. . . 4
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5 | vtocl3gf.b |
. . . . . 6
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6 | 5 | nfel1 2293 |
. . . . 5
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7 | vtocl3gf.2 |
. . . . 5
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8 | 6, 7 | nfim 1552 |
. . . 4
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9 | vtocl3gf.c |
. . . . . 6
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10 | 9 | nfel1 2293 |
. . . . 5
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11 | vtocl3gf.3 |
. . . . 5
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12 | 10, 11 | nfim 1552 |
. . . 4
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13 | vtocl3gf.5 |
. . . . 5
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14 | 13 | imbi2d 229 |
. . . 4
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15 | vtocl3gf.6 |
. . . . 5
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16 | 15 | imbi2d 229 |
. . . 4
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17 | vtocl3gf.a |
. . . . 5
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18 | vtocl3gf.1 |
. . . . 5
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19 | vtocl3gf.4 |
. . . . 5
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20 | vtocl3gf.7 |
. . . . 5
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21 | 17, 18, 19, 20 | vtoclgf 2747 |
. . . 4
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22 | 2, 3, 4, 8, 12, 14, 16, 21 | vtocl2gf 2751 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 1, 22 | mpan9 279 |
. 2
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24 | 23 | 3impb 1178 |
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-3an 965 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: vtocl3gaf 2758 |
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