Description: Selecting one statement from a disjunction if one of the disjuncted statements is false. (Contributed by AV, 6-Sep-2018) (Proof shortened by AV, 13-Oct-2018) (Proof shortened by Wolf Lammen, 19-Jan-2020)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ornld | |- ( ph -> ( ( ( ph -> ( th \/ ta ) ) /\ -. th ) -> ta ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm3.35 | |- ( ( ph /\ ( ph -> ( th \/ ta ) ) ) -> ( th \/ ta ) ) |
|
| 2 | 1 | ord | |- ( ( ph /\ ( ph -> ( th \/ ta ) ) ) -> ( -. th -> ta ) ) |
| 3 | 2 | expimpd | |- ( ph -> ( ( ( ph -> ( th \/ ta ) ) /\ -. th ) -> ta ) ) |