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| Mirrors > Home > ILE Home > Th. List > cbv2 | Unicode version | ||
| Description: Rule used to change bound variables, using implicit substitution. Revised to align format of 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 |
|---|---|
| cbv2.1 |
|
| cbv2.2 |
|
| cbv2.3 |
|
| cbv2.4 |
|
| cbv2.5 |
|
| Ref | Expression |
|---|---|
| cbv2 |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cbv2.2 |
. . . 4
| |
| 2 | 1 | nfri 1533 |
. . 3
|
| 3 | cbv2.1 |
. . . . 5
| |
| 4 | 3 | nfal 1590 |
. . . 4
|
| 5 | 4 | nfri 1533 |
. . 3
|
| 6 | 2, 5 | syl 14 |
. 2
|
| 7 | cbv2.3 |
. . . 4
| |
| 8 | 7 | nfrd 1534 |
. . 3
|
| 9 | cbv2.4 |
. . . 4
| |
| 10 | 9 | nfrd 1534 |
. . 3
|
| 11 | cbv2.5 |
. . 3
| |
| 12 | 8, 10, 11 | cbv2h 1762 |
. 2
|
| 13 | 6, 12 | syl 14 |
1
|
| 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 1461 ax-7 1462 ax-gen 1463 ax-ie1 1507 ax-ie2 1508 ax-8 1518 ax-4 1524 ax-17 1540 ax-i9 1544 ax-ial 1548 ax-i5r 1549 |
| This theorem depends on definitions: df-bi 117 df-nf 1475 |
| This theorem is referenced by: cbvald 1940 cbvrald 15434 |
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