Metamath Proof Explorer

Theorem simpr12

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof shortened by Wolf Lammen, 24-Jun-2022)

Ref Expression
Assertion simpr12 
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )

Proof

Step Hyp Ref Expression
1 simpr2 
 |-  ( ( et /\ ( ph /\ ps /\ ch ) ) -> ps )
2 1 3ad2antr1 
 |-  ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )