Table of ContentsRelated theorems
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Mathbox for Anthony Hart |
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| Description: A rederivation of nic-ax 1239 from lukshef-ax1 14161, proving that lukshef-ax1 14161 with nic-mp 1237 can be used as a complete axiomatization of propositional calculus. |
| Ref | Expression |
|---|---|
| renicax |
         |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | lukshefth1 14162 |
. . . 4
| |
| 2 | lukshefth2 14163 |
. . . 4
| |
| 3 | 1, 2 | nic-mp 1237 |
. . 3
|
| 4 | lukshefth2 14163 |
. . . 4
| |
| 5 | lukshef-ax1 14161 |
. . . 4
| |
| 6 | 4, 5 | nic-mp 1237 |
. . 3
|
| 7 | 3, 6 | nic-mp 1237 |
. 2
|
| 8 | lukshefth2 14163 |
. 2
| |
| 9 | 7, 8 | nic-mp 1237 |
1
|
| Colors of variables: wff set class |
| Syntax hints: wnand 1229 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 |
| This theorem depends on definitions: df-bi 164 df-an 242 df-nand 1230 |