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Mirrors > Home > ILE Home > Th. List > cbv1 | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. Revised to format hypotheses to common style. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Revised by Wolf Lammen, 13-May-2018.) |
Ref | Expression |
---|---|
cbv1.1 |
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cbv1.2 |
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cbv1.3 |
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cbv1.4 |
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cbv1.5 |
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Ref | Expression |
---|---|
cbv1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbv1.2 |
. . . . 5
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2 | cbv1.3 |
. . . . 5
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3 | 1, 2 | nfim1 1551 |
. . . 4
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4 | cbv1.1 |
. . . . 5
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5 | cbv1.4 |
. . . . 5
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6 | 4, 5 | nfim1 1551 |
. . . 4
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7 | cbv1.5 |
. . . . . 6
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8 | 7 | com12 30 |
. . . . 5
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9 | 8 | a2d 26 |
. . . 4
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10 | 3, 6, 9 | cbv3 1721 |
. . 3
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11 | 4 | 19.21 1563 |
. . 3
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12 | 1 | 19.21 1563 |
. . 3
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13 | 10, 11, 12 | 3imtr3i 199 |
. 2
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14 | 13 | pm2.86i 98 |
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-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-nf 1438 |
This theorem is referenced by: cbv1h 1724 |
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