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 ( 𝜑 ↔ ( 𝜓𝜒𝜃 ) )
Assertion simp1bi ( 𝜑𝜓 )

Proof

Step Hyp Ref Expression
1 3simp1bi.1 ( 𝜑 ↔ ( 𝜓𝜒𝜃 ) )
2 1 biimpi ( 𝜑 → ( 𝜓𝜒𝜃 ) )
3 2 simp1d ( 𝜑𝜓 )