Description: A more efficient proof of Theorem 5.8 of Clemente p. 20. For a longer line-by-line translation, see ex-natded5.8 . (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ex-natded5.8.1 | |- ( ph -> ( ( ps /\ ch ) -> -. th ) ) |
|
| ex-natded5.8.2 | |- ( ph -> ( ta -> th ) ) |
||
| ex-natded5.8.3 | |- ( ph -> ch ) |
||
| ex-natded5.8.4 | |- ( ph -> ta ) |
||
| Assertion | ex-natded5.8-2 | |- ( ph -> -. ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ex-natded5.8.1 | |- ( ph -> ( ( ps /\ ch ) -> -. th ) ) |
|
| 2 | ex-natded5.8.2 | |- ( ph -> ( ta -> th ) ) |
|
| 3 | ex-natded5.8.3 | |- ( ph -> ch ) |
|
| 4 | ex-natded5.8.4 | |- ( ph -> ta ) |
|
| 5 | 4 2 | mpd | |- ( ph -> th ) |
| 6 | 3 1 | mpan2d | |- ( ph -> ( ps -> -. th ) ) |
| 7 | 5 6 | mt2d | |- ( ph -> -. ps ) |