Metamath Proof Explorer

Theorem simpr33

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

Ref Expression
Assertion simpr33 
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ch )

Proof

Step Hyp Ref Expression
1 simpr3 
 |-  ( ( et /\ ( ph /\ ps /\ ch ) ) -> ch )
2 1 3ad2antr3 
 |-  ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ch )