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 | uunT11p2.1 | |- ( ( ph /\ ph /\ T. ) -> ps ) |
|
| Assertion | uunT11p2 | |- ( ph -> ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | uunT11p2.1 | |- ( ( ph /\ ph /\ T. ) -> ps ) |
|
| 2 | 3anrev | |- ( ( ph /\ ph /\ T. ) <-> ( T. /\ ph /\ ph ) ) |
|
| 3 | 3anass | |- ( ( T. /\ ph /\ ph ) <-> ( T. /\ ( ph /\ ph ) ) ) |
|
| 4 | truan | |- ( ( T. /\ ( ph /\ ph ) ) <-> ( ph /\ ph ) ) |
|
| 5 | 2 3 4 | 3bitri | |- ( ( ph /\ ph /\ T. ) <-> ( ph /\ ph ) ) |
| 6 | anidm | |- ( ( ph /\ ph ) <-> ph ) |
|
| 7 | 5 6 | bitri | |- ( ( ph /\ ph /\ T. ) <-> ph ) |
| 8 | 7 1 | sylbir | |- ( ph -> ps ) |