Metamath Proof Explorer

Theorem simpr1l

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

Ref Expression
Assertion simpr1l 
|- ( ( ta /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ph )

Proof

Step Hyp Ref Expression
1 simprl 
 |-  ( ( ta /\ ( ph /\ ps ) ) -> ph )
2 1 3ad2antr1 
 |-  ( ( ta /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ph )