Description: Inference adding a left disjunct to both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 12-Dec-2012)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | orbi2i.1 | |- ( ph <-> ps ) |
|
| Assertion | orbi2i | |- ( ( ch \/ ph ) <-> ( ch \/ ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | orbi2i.1 | |- ( ph <-> ps ) |
|
| 2 | 1 | biimpi | |- ( ph -> ps ) |
| 3 | 2 | orim2i | |- ( ( ch \/ ph ) -> ( ch \/ ps ) ) |
| 4 | 1 | biimpri | |- ( ps -> ph ) |
| 5 | 4 | orim2i | |- ( ( ch \/ ps ) -> ( ch \/ ph ) ) |
| 6 | 3 5 | impbii | |- ( ( ch \/ ph ) <-> ( ch \/ ps ) ) |