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Metamath Proof Explorer

Theorem simp-8r

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

Ref Expression
Assertion simp-8r 
|- ( ( ( ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) -> ps )

Proof

Step Hyp Ref Expression
1 id 
 |-  ( ps -> ps )
2 1 ad8antlr 
 |-  ( ( ( ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) -> ps )