Metamath Proof Explorer


Theorem imp32

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

Ref Expression
Hypothesis imp31.1 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
Assertion imp32 ( ( 𝜑 ∧ ( 𝜓𝜒 ) ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 imp31.1 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
2 1 impd ( 𝜑 → ( ( 𝜓𝜒 ) → 𝜃 ) )
3 2 imp ( ( 𝜑 ∧ ( 𝜓𝜒 ) ) → 𝜃 )