Metamath Proof Explorer


Theorem 3imp1

Description: Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005)

Ref Expression
Hypothesis 3imp1.1 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )
Assertion 3imp1 ( ( ( 𝜑𝜓𝜒 ) ∧ 𝜃 ) → 𝜏 )

Proof

Step Hyp Ref Expression
1 3imp1.1 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )
2 1 3imp ( ( 𝜑𝜓𝜒 ) → ( 𝜃𝜏 ) )
3 2 imp ( ( ( 𝜑𝜓𝜒 ) ∧ 𝜃 ) → 𝜏 )