Metamath Proof Explorer


Theorem uunT12p5

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 uunT12p5.1
|- ( ( ps /\ ph /\ T. ) -> ch )
Assertion uunT12p5
|- ( ( ph /\ ps ) -> ch )

Proof

Step Hyp Ref Expression
1 uunT12p5.1
 |-  ( ( ps /\ ph /\ T. ) -> ch )
2 3anrev
 |-  ( ( ps /\ ph /\ T. ) <-> ( T. /\ ph /\ ps ) )
3 3anass
 |-  ( ( T. /\ ph /\ ps ) <-> ( T. /\ ( ph /\ ps ) ) )
4 2 3 bitri
 |-  ( ( ps /\ ph /\ T. ) <-> ( T. /\ ( ph /\ ps ) ) )
5 truan
 |-  ( ( T. /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )
6 4 5 bitri
 |-  ( ( ps /\ ph /\ T. ) <-> ( ph /\ ps ) )
7 6 1 sylbir
 |-  ( ( ph /\ ps ) -> ch )