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Mirrors > Home > ILE Home > Th. List > cbvab | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
cbvab.1 |
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cbvab.2 |
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cbvab.3 |
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Ref | Expression |
---|---|
cbvab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvab.2 |
. . . . 5
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2 | 1 | nfsb 1882 |
. . . 4
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3 | cbvab.1 |
. . . . . 6
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4 | cbvab.3 |
. . . . . . . 8
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5 | 4 | equcoms 1652 |
. . . . . . 7
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6 | 5 | bicomd 140 |
. . . . . 6
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7 | 3, 6 | sbie 1732 |
. . . . 5
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8 | sbequ 1779 |
. . . . 5
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9 | 7, 8 | syl5bbr 193 |
. . . 4
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10 | 2, 9 | sbie 1732 |
. . 3
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11 | df-clab 2087 |
. . 3
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12 | df-clab 2087 |
. . 3
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13 | 10, 11, 12 | 3bitr4i 211 |
. 2
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14 | 13 | eqriv 2097 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 |
This theorem is referenced by: cbvabv 2223 cbvrab 2639 cbvsbc 2889 cbvrabcsf 3015 dfdmf 4670 dfrnf 4718 funfvdm2f 5418 abrexex2g 5949 abrexex2 5953 |
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