Description: The theorem form of the deduction dtrucor leads to a contradiction, as mentioned in the "Wrong!" example at mmdeduction.html#bad . Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 20-Oct-2007) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | dtrucor2.1 | |- ( x = y -> x =/= y ) |
|
| Assertion | dtrucor2 | |- ( ph /\ -. ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dtrucor2.1 | |- ( x = y -> x =/= y ) |
|
| 2 | ax6e | |- E. x x = y |
|
| 3 | 1 | necon2bi | |- ( x = y -> -. x = y ) |
| 4 | pm2.01 | |- ( ( x = y -> -. x = y ) -> -. x = y ) |
|
| 5 | 3 4 | ax-mp | |- -. x = y |
| 6 | 5 | nex | |- -. E. x x = y |
| 7 | 2 6 | pm2.24ii | |- ( ph /\ -. ph ) |