Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | uunT12p1.1 | |- ( ( T. /\ ps /\ ph ) -> ch ) |
|
| Assertion | uunT12p1 | |- ( ( ph /\ ps ) -> ch ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | uunT12p1.1 | |- ( ( T. /\ ps /\ ph ) -> ch ) |
|
| 2 | 3anass | |- ( ( T. /\ ps /\ ph ) <-> ( T. /\ ( ps /\ ph ) ) ) |
|
| 3 | truan | |- ( ( T. /\ ( ps /\ ph ) ) <-> ( ps /\ ph ) ) |
|
| 4 | 2 3 | bitri | |- ( ( T. /\ ps /\ ph ) <-> ( ps /\ ph ) ) |
| 5 | ancom | |- ( ( ph /\ ps ) <-> ( ps /\ ph ) ) |
|
| 6 | 4 5 | bitr4i | |- ( ( T. /\ ps /\ ph ) <-> ( ph /\ ps ) ) |
| 7 | 6 1 | sylbir | |- ( ( ph /\ ps ) -> ch ) |