Theorem imp5d 440

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

Hypothesis

Ref	Expression
imp5.1	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Assertion

Ref	Expression
imp5d	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → ((𝜃 ∧ 𝜏) → 𝜂))

Proof of Theorem imp5d

Step	Hyp	Ref	Expression
1		imp5.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))
2	1	imp31 418	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → (𝜃 → (𝜏 → 𝜂)))
3	2	impd 411	1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → ((𝜃 ∧ 𝜏) → 𝜂))

Syntax hints:   → wi 4   ∧ wa 396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397

This theorem is referenced by:  imp5a  441  bcthlem5  24492