Metamath Proof Explorer

Theorem simp123

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012)

Ref Expression
Assertion simp123 
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ch )

Proof

Step Hyp Ref Expression
1 simp23 
 |-  ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) -> ch )
2 1 3ad2ant1 
 |-  ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ch )