Metamath Proof Explorer


Theorem simp1d

Description: Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005)

Ref Expression
Hypothesis 3simp1d.1
|- ( ph -> ( ps /\ ch /\ th ) )
Assertion simp1d
|- ( ph -> ps )

Proof

Step Hyp Ref Expression
1 3simp1d.1
 |-  ( ph -> ( ps /\ ch /\ th ) )
2 simp1
 |-  ( ( ps /\ ch /\ th ) -> ps )
3 1 2 syl
 |-  ( ph -> ps )