Description: A disjunction is equivalent to a threefold disjunction with single falsehood of a conjunction. (Contributed by Alexander van der Vekens, 8-Sep-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | 3biorfd.1 | |- ( ph -> -. th ) |
|
| Assertion | 3bior1fand | |- ( ph -> ( ( ch \/ ps ) <-> ( ( th /\ ta ) \/ ch \/ ps ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3biorfd.1 | |- ( ph -> -. th ) |
|
| 2 | 1 | intnanrd | |- ( ph -> -. ( th /\ ta ) ) |
| 3 | 2 | 3bior1fd | |- ( ph -> ( ( ch \/ ps ) <-> ( ( th /\ ta ) \/ ch \/ ps ) ) ) |