Metamath Proof Explorer

Theorem simp3d

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

Ref Expression
Hypothesis 3simp1d.1 
|- ( ph -> ( ps /\ ch /\ th ) )
Assertion simp3d 
|- ( ph -> th )

Proof

Step Hyp Ref Expression
1 3simp1d.1 
 |-  ( ph -> ( ps /\ ch /\ th ) )
2 simp3 
 |-  ( ( ps /\ ch /\ th ) -> th )
3 1 2 syl 
 |-  ( ph -> th )