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| Mirrors > Home > NFE Home > Th. List > renicax | Unicode version | ||
| Description: A rederivation of nic-ax 1438 from lukshef-ax1 1459, proving that lukshef-ax1 1459 with nic-mp 1436 can be used as a complete axiomatization of propositional calculus. (Contributed by Anthony Hart, 31-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| renicax |
   ![](barwedge.gif "-/\"){kind=small}    
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | lukshefth1 1460 |
. . . 4
| |
| 2 | lukshefth2 1461 |
. . . 4
| |
| 3 | 1, 2 | nic-mp 1436 |
. . 3
|
| 4 | lukshefth2 1461 |
. . . 4
| |
| 5 | lukshef-ax1 1459 |
. . . 4
| |
| 6 | 4, 5 | nic-mp 1436 |
. . 3
|
| 7 | 3, 6 | nic-mp 1436 |
. 2
|
| 8 | lukshefth2 1461 |
. 2
| |
| 9 | 7, 8 | nic-mp 1436 |
1
|
| Colors of variables: wff setvar class |
| Syntax hints: wnan 1287 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
| This theorem depends on definitions: df-bi 177 df-an 360 df-nan 1288 |
| This theorem is referenced by: (None) |
| Copyright terms: Public domain | W3C validator |