Metamath Proof Explorer


Theorem imp42

Description: An importation inference. (Contributed by NM, 26-Apr-1994)

Ref Expression
Hypothesis imp4.1 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )
Assertion imp42 ( ( ( 𝜑 ∧ ( 𝜓𝜒 ) ) ∧ 𝜃 ) → 𝜏 )

Proof

Step Hyp Ref Expression
1 imp4.1 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )
2 1 imp32 ( ( 𝜑 ∧ ( 𝜓𝜒 ) ) → ( 𝜃𝜏 ) )
3 2 imp ( ( ( 𝜑 ∧ ( 𝜓𝜒 ) ) ∧ 𝜃 ) → 𝜏 )