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Mirrors > Home > ILE Home > Th. List > cbvex2 | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 14-Sep-2003.) (Revised by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
cbval2.1 |
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cbval2.2 |
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cbval2.3 |
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cbval2.4 |
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cbval2.5 |
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Ref | Expression |
---|---|
cbvex2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbval2.1 |
. . 3
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2 | 1 | nfex 1637 |
. 2
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3 | cbval2.3 |
. . 3
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4 | 3 | nfex 1637 |
. 2
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5 | nfv 1528 |
. . . . . 6
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6 | cbval2.2 |
. . . . . 6
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7 | 5, 6 | nfan 1565 |
. . . . 5
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8 | nfv 1528 |
. . . . . 6
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9 | cbval2.4 |
. . . . . 6
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10 | 8, 9 | nfan 1565 |
. . . . 5
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11 | cbval2.5 |
. . . . . . 7
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12 | 11 | expcom 116 |
. . . . . 6
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13 | 12 | pm5.32d 450 |
. . . . 5
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14 | 7, 10, 13 | cbvex 1756 |
. . . 4
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15 | 19.42v 1906 |
. . . 4
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16 | 19.42v 1906 |
. . . 4
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17 | 14, 15, 16 | 3bitr3i 210 |
. . 3
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18 | pm5.32 453 |
. . 3
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19 | 17, 18 | mpbir 146 |
. 2
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20 | 2, 4, 19 | cbvex 1756 |
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 |
This theorem depends on definitions: df-bi 117 df-nf 1461 |
This theorem is referenced by: cbvex2v 1924 cbvopab 4076 cbvoprab12 5951 |
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