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| Mirrors > Home > MPE Home > Th. List > re1tbw4 | Structured version Visualization version Unicode version | ||
| Description: tbw-ax4 1628 rederived from merco2 1661.
This theorem, along with re1tbw1 1670, re1tbw2 1671, and re1tbw3 1672, shows that merco2 1661, along with ax-mp 5, can be used as a complete axiomatization of propositional calculus. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| re1tbw4 |
      |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | re1tbw3 1672 |
. . 3
| |
| 2 | re1tbw2 1671 |
. . . 4
| |
| 3 | re1tbw1 1670 |
. . . 4
| |
| 4 | 2, 3 | ax-mp 5 |
. . 3
|
| 5 | 1, 4 | ax-mp 5 |
. 2
|
| 6 | re1tbw3 1672 |
. . . . 5
| |
| 7 | re1tbw2 1671 |
. . . . . 6
| |
| 8 | re1tbw1 1670 |
. . . . . 6
| |
| 9 | 7, 8 | ax-mp 5 |
. . . . 5
|
| 10 | 6, 9 | ax-mp 5 |
. . . 4
|
| 11 | mercolem3 1664 |
. . . . 5
| |
| 12 | merco2 1661 |
. . . . 5
| |
| 13 | 11, 12 | ax-mp 5 |
. . . 4
|
| 14 | 10, 13 | ax-mp 5 |
. . 3
|
| 15 | 5, 14 | ax-mp 5 |
. 2
|
| 16 | 5, 15 | ax-mp 5 |
1
|
| Colors of variables: wff setvar class |
| Syntax hints: wi 4
wfal 1488 |
| 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 197 df-tru 1486 df-fal 1489 |
| This theorem is referenced by: (None) |
| Copyright terms: Public domain | W3C validator |