Metamath Proof Explorer

Theorem simpr31

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

Ref Expression
Assertion simpr31 
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ph )

Proof

Step Hyp Ref Expression
1 simpr1 
 |-  ( ( et /\ ( ph /\ ps /\ ch ) ) -> ph )
2 1 3ad2antr3 
 |-  ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ph )