Metamath Proof Explorer


Theorem simp3d

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

Ref Expression
Hypothesis 3simp1d.1 ( 𝜑 → ( 𝜓𝜒𝜃 ) )
Assertion simp3d ( 𝜑𝜃 )

Proof

Step Hyp Ref Expression
1 3simp1d.1 ( 𝜑 → ( 𝜓𝜒𝜃 ) )
2 simp3 ( ( 𝜓𝜒𝜃 ) → 𝜃 )
3 1 2 syl ( 𝜑𝜃 )