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| Mirrors > Home > MPE Home > Th. List > Mathboxes > axc5c4c711toc7 | Structured version Unicode version | |
| Description: Re-derivation of axc7 1913 from axc5c4c711 36616. Note that neither axc7 1913 nor ax-11 1893 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 1681 |
. . . . . . 7
|
| 3 | 2 | axc4i 1954 |
. . . . . 6
|
| 4 | 3 | con3i 141 |
. . . . 5
|
| 5 | 4 | alimi 1681 |
. . . 4
|
| 6 | 5 | sps 1917 |
. . 3
|
| 7 | 6 | con3i 141 |
. 2
|
| 8 | pm2.21 112 |
. . . 4
| |
| 9 | axc5c4c711 36616 |
. . . 4
| |
| 10 | 8, 9 | syl 17 |
. . 3
|
| 11 | sp 1911 |
. . 3
| |
| 12 | 10, 11 | syl6 35 |
. 2
|
| 13 | pm2.27 41 |
. . 3
| |
| 14 | id 23 |
. . 3
| |
| 15 | 13, 14 | mpg 1668 |
. 2
|
| 16 | 7, 12, 15 | 3syl 18 |
1
|
| Colors of variables: wff setvar class |
| Syntax hints: wn 3
wi 4
wal 1436 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1666 ax-4 1679 ax-5 1749 ax-6 1795 ax-7 1840 ax-10 1888 ax-11 1893 ax-12 1906 |
| This theorem depends on definitions: df-bi 189 df-ex 1661 df-nf 1665 |
| This theorem is referenced by: axc5c4c711to11 36620 |
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