Metamath Proof Explorer

Theorem simprl1

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof shortened by Wolf Lammen, 23-Jun-2022)

Ref Expression
Assertion simprl1 
|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ph )

Proof

Step Hyp Ref Expression
1 simp1 
 |-  ( ( ph /\ ps /\ ch ) -> ph )
2 1 ad2antrl 
 |-  ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ph )