Metamath Proof Explorer

Theorem simpl21

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

Ref Expression
Assertion simpl21 
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et ) -> ph )

Proof

Step Hyp Ref Expression
1 simpl1 
 |-  ( ( ( ph /\ ps /\ ch ) /\ et ) -> ph )
2 1 3ad2antl2 
 |-  ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et ) -> ph )