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Mirrors > Home > ILE Home > Th. List > vtocl2 | Unicode version |
Description: Implicit substitution of classes for setvar variables. (Contributed by NM, 26-Jul-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
vtocl2.1 |
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vtocl2.2 |
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vtocl2.3 |
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vtocl2.4 |
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Ref | Expression |
---|---|
vtocl2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocl2.1 |
. . . . . 6
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2 | 1 | isseti 2746 |
. . . . 5
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3 | vtocl2.2 |
. . . . . 6
![]() ![]() ![]() ![]() | |
4 | 3 | isseti 2746 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
5 | eeanv 1932 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | vtocl2.3 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | biimpd 144 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 7 | 2eximi 1601 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | 5, 8 | sylbir 135 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 2, 4, 9 | mp2an 426 |
. . . 4
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11 | nfv 1528 |
. . . . 5
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12 | 11 | 19.36-1 1673 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | 10, 12 | eximii 1602 |
. . 3
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14 | 13 | 19.36aiv 1901 |
. 2
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15 | vtocl2.4 |
. . 3
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16 | 15 | ax-gen 1449 |
. 2
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17 | 14, 16 | mpg 1451 |
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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-v 2740 |
This theorem is referenced by: undifexmid 4194 caovord 6046 ctssexmid 7148 |
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