Metamath Proof Explorer


Theorem simp-12r

Description: Simplification of a conjunction. (Contributed by Thierry Arnoux, 5-Oct-2025)

Ref Expression
Assertion simp-12r
|- ( ( ( ( ( ( ( ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) /\ mu ) /\ la ) /\ ka ) /\ nu ) -> ps )

Proof

Step Hyp Ref Expression
1 simpr
 |-  ( ( ph /\ ps ) -> ps )
2 1 ad11antr
 |-  ( ( ( ( ( ( ( ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) /\ mu ) /\ la ) /\ ka ) /\ nu ) -> ps )