Metamath Proof Explorer


Theorem simp1i

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005)

Ref Expression
Hypothesis 3simp1i.1
|- ( ph /\ ps /\ ch )
Assertion simp1i
|- ph

Proof

Step Hyp Ref Expression
1 3simp1i.1
 |-  ( ph /\ ps /\ ch )
2 simp1
 |-  ( ( ph /\ ps /\ ch ) -> ph )
3 1 2 ax-mp
 |-  ph