Metamath Proof Explorer

Theorem simpr21

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

Ref Expression
Assertion simpr21 
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ph )

Proof

Step Hyp Ref Expression
1 simpr1 
 |-  ( ( et /\ ( ph /\ ps /\ ch ) ) -> ph )
2 1 3ad2antr2 
 |-  ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ph )