Metamath Proof Explorer


Theorem imp43

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

Ref Expression
Hypothesis imp4.1 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )
Assertion imp43 ( ( ( 𝜑𝜓 ) ∧ ( 𝜒𝜃 ) ) → 𝜏 )

Proof

Step Hyp Ref Expression
1 imp4.1 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )
2 1 imp4b ( ( 𝜑𝜓 ) → ( ( 𝜒𝜃 ) → 𝜏 ) )
3 2 imp ( ( ( 𝜑𝜓 ) ∧ ( 𝜒𝜃 ) ) → 𝜏 )