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 | uunT12p4.1 | |- ( ( ph /\ ps /\ T. ) -> ch ) |
|
Assertion | uunT12p4 | |- ( ( ph /\ ps ) -> ch ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uunT12p4.1 | |- ( ( ph /\ ps /\ T. ) -> ch ) |
|
2 | 3anrot | |- ( ( T. /\ ph /\ ps ) <-> ( ph /\ ps /\ T. ) ) |
|
3 | 3anass | |- ( ( T. /\ ph /\ ps ) <-> ( T. /\ ( ph /\ ps ) ) ) |
|
4 | 2 3 | bitr3i | |- ( ( ph /\ ps /\ T. ) <-> ( T. /\ ( ph /\ ps ) ) ) |
5 | truan | |- ( ( T. /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) ) |
|
6 | 4 5 | bitri | |- ( ( ph /\ ps /\ T. ) <-> ( ph /\ ps ) ) |
7 | 6 1 | sylbir | |- ( ( ph /\ ps ) -> ch ) |