Description: Inference removing a negated conjunct in a disjunction of an antecedent if this conjunct is part of the disjunction. (Contributed by Alexander van der Vekens, 3-Nov-2017) (Proof shortened by Wolf Lammen, 21-Sep-2018)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | jaoi2.1 | |- ( ( ph \/ ( -. ph /\ ch ) ) -> ps ) |
|
| Assertion | jaoi2 | |- ( ( ph \/ ch ) -> ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | jaoi2.1 | |- ( ( ph \/ ( -. ph /\ ch ) ) -> ps ) |
|
| 2 | pm5.63 | |- ( ( ph \/ ch ) <-> ( ph \/ ( -. ph /\ ch ) ) ) |
|
| 3 | 2 1 | sylbi | |- ( ( ph \/ ch ) -> ps ) |