Metamath Proof Explorer

Theorem simp-7r

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

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

Proof

Step Hyp Ref Expression
1 id 
 |-  ( ps -> ps )
2 1 ad7antlr 
 |-  ( ( ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) -> ps )