Metamath Proof Explorer

Theorem simp1bi

Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

Ref Expression
Hypothesis 3simp1bi.1 
|- ( ph <-> ( ps /\ ch /\ th ) )
Assertion simp1bi 
|- ( ph -> ps )

Proof

Step Hyp Ref Expression
1 3simp1bi.1 
 |-  ( ph <-> ( ps /\ ch /\ th ) )
2 1 biimpi 
 |-  ( ph -> ( ps /\ ch /\ th ) )
3 2 simp1d 
 |-  ( ph -> ps )