Theorem imp511 446

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
imp511	⊢ ((𝜑 ∧ ((𝜓 ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏)) → 𝜂)

Proof of Theorem imp511

Step	Hyp	Ref	Expression
1		imp5.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))
2	1	imp4a 425	. 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → (𝜏 → 𝜂))))
3	2	imp44 431	1 ⊢ ((𝜑 ∧ ((𝜓 ∧ (𝜒 ∧ 𝜃)) ∧ 𝜏)) → 𝜂)

Syntax hints:   → wi 4   ∧ wa 398

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 209  df-an 399

This theorem is referenced by: (None)