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| Mirrors > Home > MPE Home > Th. List > Mathboxes > axc5c4c711toc7 | Structured version Visualization version Unicode version | ||
| Description: Rederivation of axc7 2132 from axc5c4c711 38602. Note that neither axc7 2132 nor ax-11 2034 are required for the rederivation. (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 1739 |
. . . . . . 7
|
| 3 | 2 | axc4i 2131 |
. . . . . 6
|
| 4 | 3 | con3i 150 |
. . . . 5
|
| 5 | 4 | alimi 1739 |
. . . 4
|
| 6 | 5 | sps 2055 |
. . 3
|
| 7 | 6 | con3i 150 |
. 2
|
| 8 | pm2.21 120 |
. . . 4
| |
| 9 | axc5c4c711 38602 |
. . . 4
| |
| 10 | 8, 9 | syl 17 |
. . 3
|
| 11 | sp 2053 |
. . 3
| |
| 12 | 10, 11 | syl6 35 |
. 2
|
| 13 | pm2.27 42 |
. . 3
| |
| 14 | id 22 |
. . 3
| |
| 15 | 13, 14 | mpg 1724 |
. 2
|
| 16 | 7, 12, 15 | 3syl 18 |
1
|
| Colors of variables: wff setvar class |
| Syntax hints: wn 3
wi 4
wal 1481 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 |
| This theorem depends on definitions: df-bi 197 df-or 385 df-ex 1705 df-nf 1710 |
| This theorem is referenced by: axc5c4c711to11 38606 |
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