Nearby theorems
|
|
Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
|
| Mirrors > Home > MPE Home > Th. List > Mathboxes > ee233 | Structured version Visualization version Unicode version | ||
Description: Non-virtual deduction form of e233 37191. (Contributed by Alan Sare,
18-Mar-2012.)
(Proof modification is discouraged.) (New usage is discouraged.)
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. The
completed Virtual
Deduction Proof (not shown) was minimized. The minimized proof is
shown.
|
| Ref | Expression |
|---|---|
| ee233.1 |
       |
| ee233.2 |
  |
| ee233.3 |
 |
| ee233.4 |
 |
| Ref | Expression |
|---|---|
| ee233 |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ee233.3 |
. . . . 5
| |
| 2 | ee233.2 |
. . . . . . . . 9
| |
| 3 | ee233.1 |
. . . . . . . . . . 11
| |
| 4 | ee233.4 |
. . . . . . . . . . 11
| |
| 5 | 3, 4 | syl6 34 |
. . . . . . . . . 10
|
| 6 | 5 | com3r 82 |
. . . . . . . . 9
|
| 7 | 2, 6 | syl8 72 |
. . . . . . . 8
|
| 8 | pm2.43cbi 36918 |
. . . . . . . 8
| |
| 9 | 7, 8 | mpbi 213 |
. . . . . . 7
|
| 10 | pm2.43cbi 36918 |
. . . . . . 7
| |
| 11 | 9, 10 | mpbi 213 |
. . . . . 6
|
| 12 | 11 | com14 91 |
. . . . 5
|
| 13 | 1, 12 | syl8 72 |
. . . 4
|
| 14 | pm2.43cbi 36918 |
. . . 4
| |
| 15 | 13, 14 | mpbi 213 |
. . 3
|
| 16 | pm2.43cbi 36918 |
. . 3
| |
| 17 | 15, 16 | mpbi 213 |
. 2
|
| 18 | pm2.43cbi 36918 |
. 2
| |
| 19 | 17, 18 | mpbi 213 |
1
|
| Colors of variables: wff setvar class |
| Syntax hints: wi 4 |
| 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 190 |
| This theorem is referenced by: truniALT 36945 onfrALTlem2 36955 e233 37191 |
| Copyright terms: Public domain | W3C validator |