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 | uunTT1p2.1 | |- ( ( ph /\ T. /\ T. ) -> ps ) |
|
Assertion | uunTT1p2 | |- ( ph -> ps ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uunTT1p2.1 | |- ( ( ph /\ T. /\ T. ) -> ps ) |
|
2 | 3anrot | |- ( ( ph /\ T. /\ T. ) <-> ( T. /\ T. /\ ph ) ) |
|
3 | 3anass | |- ( ( T. /\ T. /\ ph ) <-> ( T. /\ ( T. /\ ph ) ) ) |
|
4 | anabs5 | |- ( ( T. /\ ( T. /\ ph ) ) <-> ( T. /\ ph ) ) |
|
5 | 2 3 4 | 3bitri | |- ( ( ph /\ T. /\ T. ) <-> ( T. /\ ph ) ) |
6 | truan | |- ( ( T. /\ ph ) <-> ph ) |
|
7 | 5 6 | bitri | |- ( ( ph /\ T. /\ T. ) <-> ph ) |
8 | 7 1 | sylbir | |- ( ph -> ps ) |