Metamath Proof Explorer


Theorem imp5g

Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009)

Ref Expression
Hypothesis imp5.1 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) ) ) )
Assertion imp5g ( ( 𝜑𝜓 ) → ( ( ( 𝜒𝜃 ) ∧ 𝜏 ) → 𝜂 ) )

Proof

Step Hyp Ref Expression
1 imp5.1 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) ) ) )
2 1 imp4b ( ( 𝜑𝜓 ) → ( ( 𝜒𝜃 ) → ( 𝜏𝜂 ) ) )
3 2 impd ( ( 𝜑𝜓 ) → ( ( ( 𝜒𝜃 ) ∧ 𝜏 ) → 𝜂 ) )