Metamath Proof Explorer

Theorem simpl31

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

Ref Expression
Assertion simpl31 
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ph )

Proof

Step Hyp Ref Expression
1 simpl1 
 |-  ( ( ( ph /\ ps /\ ch ) /\ et ) -> ph )
2 1 3ad2antl3 
 |-  ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ph )