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| Mirrors > Home > MPE Home > Th. List > Mathboxes > axc5c711toc7 | Structured version Visualization version Unicode version | ||
| Description: Rederivation of ax-c7 34170 from axc5c711 34203. Note that ax-c7 34170 and ax-11 2034 are not used by the rederivation. The use of alimi 1739 (which uses ax-c5 34168) is allowed since we have already proved axc5c711toc5 34204. (Contributed by NM, 19-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| axc5c711toc7 |
      
 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hba1-o 34182 |
. . . . . 6
| |
| 2 | 1 | con3i 150 |
. . . . 5
|
| 3 | 2 | alimi 1739 |
. . . 4
|
| 4 | 3 | sps-o 34193 |
. . 3
|
| 5 | 4 | con3i 150 |
. 2
|
| 6 | pm2.21 120 |
. 2
| |
| 7 | axc5c711 34203 |
. 2
| |
| 8 | 5, 6, 7 | 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-11 2034 ax-c5 34168 ax-c4 34169 ax-c7 34170 |
| This theorem is referenced by: axc5c711to11 34206 |
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