Metamath Proof Explorer


Theorem simp3bi

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

Ref Expression
Hypothesis 3simp1bi.1 ( 𝜑 ↔ ( 𝜓𝜒𝜃 ) )
Assertion simp3bi ( 𝜑𝜃 )

Proof

Step Hyp Ref Expression
1 3simp1bi.1 ( 𝜑 ↔ ( 𝜓𝜒𝜃 ) )
2 1 biimpi ( 𝜑 → ( 𝜓𝜒𝜃 ) )
3 2 simp3d ( 𝜑𝜃 )