Description: Theorem *4.14 of WhiteheadRussell p. 117. Related to con34b . (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 23-Oct-2012)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | pm4.14 | |- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ph /\ -. ch ) -> -. ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | con34b | |- ( ( ps -> ch ) <-> ( -. ch -> -. ps ) ) |
|
| 2 | 1 | imbi2i | |- ( ( ph -> ( ps -> ch ) ) <-> ( ph -> ( -. ch -> -. ps ) ) ) |
| 3 | impexp | |- ( ( ( ph /\ ps ) -> ch ) <-> ( ph -> ( ps -> ch ) ) ) |
|
| 4 | impexp | |- ( ( ( ph /\ -. ch ) -> -. ps ) <-> ( ph -> ( -. ch -> -. ps ) ) ) |
|
| 5 | 2 3 4 | 3bitr4i | |- ( ( ( ph /\ ps ) -> ch ) <-> ( ( ph /\ -. ch ) -> -. ps ) ) |