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| Mirrors > Home > MPE Home > Th. List > Mathboxes > axc5c4c711toc7 | Structured version Unicode version | |
| Description: Re-derivation of axc7 1862 from axc5c4c711 31512. Note that neither axc7 1862 nor ax-11 1843 are required for the re-derivation. (Contributed by Andrew Salmon, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| axc5c4c711toc7 |
      
 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-1 6 |
. . . . . . . 8
| |
| 2 | 1 | alimi 1634 |
. . . . . . 7
|
| 3 | 2 | axc4i 1899 |
. . . . . 6
|
| 4 | 3 | con3i 135 |
. . . . 5
|
| 5 | 4 | alimi 1634 |
. . . 4
|
| 6 | 5 | sps 1866 |
. . 3
|
| 7 | 6 | con3i 135 |
. 2
|
| 8 | pm2.21 108 |
. . . 4
| |
| 9 | axc5c4c711 31512 |
. . . 4
| |
| 10 | 8, 9 | syl 16 |
. . 3
|
| 11 | sp 1860 |
. . 3
| |
| 12 | 10, 11 | syl6 33 |
. 2
|
| 13 | pm2.27 39 |
. . 3
| |
| 14 | id 22 |
. . 3
| |
| 15 | 13, 14 | mpg 1621 |
. 2
|
| 16 | 7, 12, 15 | 3syl 20 |
1
|
| Colors of variables: wff setvar class |
| Syntax hints: wn 3
wi 4
wal 1393 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1619 ax-4 1632 ax-5 1705 ax-6 1748 ax-7 1791 ax-10 1838 ax-11 1843 ax-12 1855 |
| This theorem depends on definitions: df-bi 185 df-ex 1614 df-nf 1618 |
| This theorem is referenced by: axc5c4c711to11 31516 |
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