Description: A more efficient proof of Theorem 5.13 of Clemente p. 20. Compare with ex-natded5.13 . (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ex-natded5.13.1 | |- ( ph -> ( ps \/ ch ) ) |
|
| ex-natded5.13.2 | |- ( ph -> ( ps -> th ) ) |
||
| ex-natded5.13.3 | |- ( ph -> ( -. ta -> -. ch ) ) |
||
| Assertion | ex-natded5.13-2 | |- ( ph -> ( th \/ ta ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ex-natded5.13.1 | |- ( ph -> ( ps \/ ch ) ) |
|
| 2 | ex-natded5.13.2 | |- ( ph -> ( ps -> th ) ) |
|
| 3 | ex-natded5.13.3 | |- ( ph -> ( -. ta -> -. ch ) ) |
|
| 4 | 3 | con4d | |- ( ph -> ( ch -> ta ) ) |
| 5 | 2 4 | orim12d | |- ( ph -> ( ( ps \/ ch ) -> ( th \/ ta ) ) ) |
| 6 | 1 5 | mpd | |- ( ph -> ( th \/ ta ) ) |