Metamath Proof Explorer

Theorem simp-7l

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 24-May-2022)

Ref Expression
Assertion simp-7l 
|- ( ( ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) -> ph )

Proof

Step Hyp Ref Expression
1 id 
 |-  ( ph -> ph )
2 1 ad7antr 
 |-  ( ( ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) -> ph )