Metamath Proof Explorer

Theorem simp22

Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011)

Ref Expression
Assertion simp22 
|- ( ( ph /\ ( ps /\ ch /\ th ) /\ ta ) -> ch )

Proof

Step Hyp Ref Expression
1 simp2 
 |-  ( ( ps /\ ch /\ th ) -> ch )
2 1 3ad2ant2 
 |-  ( ( ph /\ ( ps /\ ch /\ th ) /\ ta ) -> ch )