Description: Obsolete version of bian1d as of 29-Jun-2025. (Contributed by Thierry Arnoux, 26-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | bian1d.1 | |- ( ph -> ( ps <-> ( ch /\ th ) ) ) |
|
| Assertion | bian1dOLD | |- ( ph -> ( ( ch /\ ps ) <-> ( ch /\ th ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bian1d.1 | |- ( ph -> ( ps <-> ( ch /\ th ) ) ) |
|
| 2 | 1 | biimpd | |- ( ph -> ( ps -> ( ch /\ th ) ) ) |
| 3 | 2 | adantld | |- ( ph -> ( ( ch /\ ps ) -> ( ch /\ th ) ) ) |
| 4 | simpl | |- ( ( ch /\ th ) -> ch ) |
|
| 5 | 4 | a1i | |- ( ph -> ( ( ch /\ th ) -> ch ) ) |
| 6 | 1 | biimprd | |- ( ph -> ( ( ch /\ th ) -> ps ) ) |
| 7 | 5 6 | jcad | |- ( ph -> ( ( ch /\ th ) -> ( ch /\ ps ) ) ) |
| 8 | 3 7 | impbid | |- ( ph -> ( ( ch /\ ps ) <-> ( ch /\ th ) ) ) |